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Stochastic Differential Equations And Applications

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Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications Book
Author : X Mao
Publisher : Elsevier
Release : 2007-12-30
ISBN : 085709940X
Language : En, Es, Fr & De

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Book Description :

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications Book
Author : Avner Friedman
Publisher : Academic Press
Release : 2014-06-20
ISBN : 1483217876
Language : En, Es, Fr & De

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Book Description :

Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

Stochastic Differential Equations

Stochastic Differential Equations Book
Author : Bernt Oksendal
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 3662025744
Language : En, Es, Fr & De

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Book Description :

From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2

Theory of Stochastic Differential Equations with Jumps and Applications

Theory of Stochastic Differential Equations with Jumps and Applications Book
Author : Rong SITU
Publisher : Springer Science & Business Media
Release : 2006-05-06
ISBN : 0387251758
Language : En, Es, Fr & De

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Book Description :

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance Book
Author : Carlos A. Braumann
Publisher : John Wiley & Sons
Release : 2019-03-08
ISBN : 1119166071
Language : En, Es, Fr & De

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Book Description :

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Forward Backward Stochastic Differential Equations and their Applications

Forward Backward Stochastic Differential Equations and their Applications Book
Author : Jin Ma,Jiongmin Yong
Publisher : Springer
Release : 2007-04-24
ISBN : 3540488316
Language : En, Es, Fr & De

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Book Description :

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications Book
Author : Kai Liu
Publisher : CRC Press
Release : 2005-08-23
ISBN : 1420034820
Language : En, Es, Fr & De

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Book Description :

Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ

Stochastic Differential Equations and Their Applications

Stochastic Differential Equations and Their Applications Book
Author : Xuerong Mao
Publisher : ISBS
Release : 1997
ISBN : 9781898563266
Language : En, Es, Fr & De

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Book Description :

Download Stochastic Differential Equations and Their Applications book written by Xuerong Mao, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications Book
Author : Łukasz Delong
Publisher : Springer Science & Business Media
Release : 2013-06-12
ISBN : 1447153316
Language : En, Es, Fr & De

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Book Description :

Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.

Stochastic Partial Differential Equations and Applications

Stochastic Partial Differential Equations and Applications Book
Author : Giuseppe Da Prato,Luciano Tubaro
Publisher : Springer
Release : 2006-11-15
ISBN : 3540474080
Language : En, Es, Fr & De

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Book Description :

Download Stochastic Partial Differential Equations and Applications book written by Giuseppe Da Prato,Luciano Tubaro, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Stochastic Differential Equations

Stochastic Differential Equations Book
Author : K. Sobczyk
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 9401137129
Language : En, Es, Fr & De

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Book Description :

'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl!be~ IbcII _t to!be dusty cauialcr Iabc & d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely.

Stochastic Differential Equations in Infinite Dimensions

Stochastic Differential Equations in Infinite Dimensions Book
Author : Leszek Gawarecki,Vidyadhar Mandrekar
Publisher : Springer Science & Business Media
Release : 2010-11-29
ISBN : 3642161944
Language : En, Es, Fr & De

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Book Description :

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations Book
Author : Simo Särkkä,Arno Solin
Publisher : Cambridge University Press
Release : 2019-04-30
ISBN : 1316510085
Language : En, Es, Fr & De

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Book Description :

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of It calculus, the central theorems in the field, and such approximation schemes as stochastic Runge-Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.

Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations Book
Author : Peter E. Kloeden,Eckhard Platen
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 3662126168
Language : En, Es, Fr & De

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Book Description :

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations Book
Author : Lawrence C. Evans
Publisher : American Mathematical Soc.
Release : 2012-12-11
ISBN : 1470410540
Language : En, Es, Fr & De

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Book Description :

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

Modeling with It Stochastic Differential Equations

Modeling with It   Stochastic Differential Equations Book
Author : E. Allen
Publisher : Springer Science & Business Media
Release : 2007-03-08
ISBN : 1402059531
Language : En, Es, Fr & De

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Book Description :

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.

Stochastic Differential Equations

Stochastic Differential Equations Book
Author : Michael J. Panik
Publisher : John Wiley & Sons
Release : 2017-03-15
ISBN : 1119377404
Language : En, Es, Fr & De

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Book Description :

A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

Backward Stochastic Differential Equations

Backward Stochastic Differential Equations Book
Author : Jianfeng Zhang
Publisher : Springer
Release : 2017-08-22
ISBN : 1493972561
Language : En, Es, Fr & De

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Book Description :

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Stochastic Differential Inclusions and Applications

Stochastic Differential Inclusions and Applications Book
Author : Michał Kisielewicz
Publisher : Springer Science & Business Media
Release : 2013-06-12
ISBN : 146146756X
Language : En, Es, Fr & De

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Book Description :

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Theory and Applications of Stochastic Differential Equations

Theory and Applications of Stochastic Differential Equations Book
Author : Zeev Schuss
Publisher : John Wiley & Sons Incorporated
Release : 1980
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.