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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 : ISBS
Release : 2008-01-13
ISBN : 9781904275343
Language : En, Es, Fr & De

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Book Description :

Mao (statistics and modeling science, U. of Strathclyde) has thoroughly revised this advanced undergraduate and graduate text, in part to describe several popular stochastic models and applications in population systems and finance. He covers generalized Gronwall inequality and Bihari inequality, Brownian motions and stochastic intervals, analysis of Ito and Feynman-Kac formulas, the Ruzumikhin technique of the Lyapunov method, approximate solutions to stochastic differential equations according to Cauchy-Marayama and Carathedory methods. Appropriate for pure and applied mathematicians, statisticians, engineers in control and communications, information scientists, physicists and economists. Previously published under title Stochastic Differential Equations and their Applications in 1997. Distributed by ISBS. Annotation ³2009 Book News, Inc., Portland, OR (booknews.com)

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 : 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.

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 : Wiley
Release : 2019-04-29
ISBN : 1119166063
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.

Stochastic Partial Differential Equations and Applications VII

Stochastic Partial Differential Equations and Applications   VII Book
Author : Giuseppe Da Prato
Publisher : Chapman & Hall/CRC
Release : 2017-08-09
ISBN : 9781138417519
Language : En, Es, Fr & De

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Book Description :

Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this book presents valuable information for PhD students in probability and PDEs as well as for researchers in pure and applied mathematics. Coverage includes Navier-Stokes equations, Ornstein-Uhlenbeck semigroups, quantum stochastic differential equations, applications of SPDE, 3D stochastic Navier-Stokes equations, and nonlinear filtering.

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.

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

Stochastic Differential Equations

Stochastic Differential Equations Book
Author : Ludwig Arnold,LUDWIG AUTOR ARNOLD
Publisher : Wiley-Interscience
Release : 1974-04-23
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Fundamentals of probability theory; Markov processes and diffusion processes; Wiener process and white noise; Stochastic integrals; The stochastic integral as a stochastic process, stochastic differentials; Stochastic differential equations, existence and uniqueness of solutions; Properties of the solutions of stochastic differential equations; Linear stochastic differentials equations; The solutions of stochastic differentail equations as Markov and diffusion processes; Questions of modeling and approximation; Stability of stochastic dynamic systems; Optimal filtering of a disturbed signal; Optimal control of stochastic dynamic systems.

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).

Reflecting Stochastic Differential Equations with Jumps and Applications

Reflecting Stochastic Differential Equations with Jumps and Applications Book
Author : Situ Rong
Publisher : CRC Press
Release : 1999-08-05
ISBN : 9781584881254
Language : En, Es, Fr & De

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Book Description :

Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.

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
Publisher : Unknown
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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

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.

Stochastic Differential Equations

Stochastic Differential Equations Book
Author : Bernt Øksendal
Publisher : Springer Science & Business Media
Release : 2003
ISBN : 9783540047582
Language : En, Es, Fr & De

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Book Description :

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.

Stochastic Partial Differential Equations and Applications II

Stochastic Partial Differential Equations and Applications II Book
Author : Giuseppe Da Prato
Publisher : Springer Verlag
Release : 1989-08-09
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.

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.

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

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 : 9781420034820
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 Applications

Stochastic Differential Equations and Applications Book
Author : Avner Friedman
Publisher : Unknown
Release : 1975
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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

Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications Book
Author : Brian Lenoach
Publisher : Unknown
Release : 1983
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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