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An Introduction To Stochastic Orders

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An Introduction to Stochastic Orders

An Introduction to Stochastic Orders Book
Author : Felix Belzunce,Carolina Martinez Riquelme,Julio Mulero
Publisher : Academic Press
Release : 2015-09-29
ISBN : 0128038268
Language : En, Es, Fr & De

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Book Description :

An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models. Introduces stochastic orders and its notation Discusses different orders of univariate stochastic orders Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders

An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling Book
Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483269272
Language : En, Es, Fr & De

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Book Description :

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Introduction to Stochastic Processes

Introduction to Stochastic Processes Book
Author : Erhan Cinlar
Publisher : Courier Corporation
Release : 2013-02-20
ISBN : 0486276325
Language : En, Es, Fr & De

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Book Description :

Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.

Introduction to Stochastic Processes with R

Introduction to Stochastic Processes with R Book
Author : Robert P. Dobrow
Publisher : John Wiley & Sons
Release : 2016-03-07
ISBN : 1118740653
Language : En, Es, Fr & De

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Book Description :

An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical freeware R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: Over 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and interesting supplemental topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black-Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion website that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.

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).

Introduction to Stochastic Dynamic Programming

Introduction to Stochastic Dynamic Programming Book
Author : Sheldon M. Ross
Publisher : Academic Press
Release : 2014-07-10
ISBN : 1483269094
Language : En, Es, Fr & De

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Book Description :

Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

Combining Soft Computing and Statistical Methods in Data Analysis

Combining Soft Computing and Statistical Methods in Data Analysis Book
Author : Christian Borgelt,Gil González Rodríguez,Wolfgang Trutschnig,María Asunción Lubiano,María Angeles Gil,Przemyslaw Grzegorzewski,Olgierd Hryniewicz
Publisher : Springer Science & Business Media
Release : 2010-10-12
ISBN : 3642147461
Language : En, Es, Fr & De

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Book Description :

Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

Stochastic Processes

Stochastic Processes Book
Author : Peter Watts Jones,Peter Smith
Publisher : CRC Press
Release : 2017-10-30
ISBN : 1498778127
Language : En, Es, Fr & De

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Book Description :

Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues. The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference. This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.

An Introduction to Stochastic Processes and Their Applications

An Introduction to Stochastic Processes and Their Applications Book
Author : Petar Todorovic
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461397421
Language : En, Es, Fr & De

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Book Description :

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro vided in Chapter 1. This chapter also contains a number of motivating ex amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.

Stochastic Processes with Applications

Stochastic Processes with Applications Book
Author : Antonio Di Crescenzo,Claudio Macci,Barbara Martinucci
Publisher : MDPI
Release : 2019-11-28
ISBN : 3039217283
Language : En, Es, Fr & De

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Book Description :

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines. This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.

Introduction to Stochastic Models

Introduction to Stochastic Models Book
Author : Roe Goodman
Publisher : Courier Corporation
Release : 1988
ISBN : 0486450376
Language : En, Es, Fr & De

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Book Description :

Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state probabilities, general queuing systems, and renewal processes. Each section features worked examples, and exercises appear at the end of each chapter, with numerical solutions at the back of the book. Suggestions for further reading in stochastic processes, simulation, and various applications also appear at the end.

Stochastic Finance

Stochastic Finance Book
Author : Nicolas Privault
Publisher : CRC Press
Release : 2013-12-20
ISBN : 1466594020
Language : En, Es, Fr & De

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Book Description :

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

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 Ordering and Dependence in Applied Probability

Stochastic Ordering and Dependence in Applied Probability Book
Author : R. Szekli
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461225280
Language : En, Es, Fr & De

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Book Description :

This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re newal processes, then results on stochastic ordering of networks, re~~ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem plified by results on queueing networks and point processes among others.

Stochastic Orders

Stochastic Orders Book
Author : Moshe Shaked,J. George Shanthikumar
Publisher : Springer Science & Business Media
Release : 2007-04-03
ISBN : 0387346759
Language : En, Es, Fr & De

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Book Description :

This reference text presents comprehensive coverage of the various notions of stochastic orderings, their closure properties, and their applications. Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields. And the value of the other notions of stochastic orderings needs further exploration. This book is an ideal reference for those interested in decision making under uncertainty and interested in the analysis of complex stochastic systems. It is suitable as a text for advanced graduate course on stochastic ordering and applications.

Stochastic Orders in Reliability and Risk

Stochastic Orders in Reliability and Risk Book
Author : Haijun Li,Xiaohu Li
Publisher : Springer Science & Business Media
Release : 2013-06-22
ISBN : 1461468922
Language : En, Es, Fr & De

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Book Description :

Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference’s talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.

Stochastic Orders and Decision Under Risk

Stochastic Orders and Decision Under Risk Book
Author : Karl C. Mosler
Publisher : IMS
Release : 1991
ISBN : 9780940600263
Language : En, Es, Fr & De

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Book Description :

Download Stochastic Orders and Decision Under Risk book written by Karl C. Mosler, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to Stochastic Processes

Introduction to Stochastic Processes Book
Author : Paul G. Hoel,Sidney C. Port,Charles J. Stone
Publisher : Waveland Press
Release : 1986-12-01
ISBN : 1478608994
Language : En, Es, Fr & De

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Book Description :

An excellent introduction for computer scientists and electrical and electronics engineers who would like to have a good, basic understanding of stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.

Stochastic Processes with R

Stochastic Processes with R Book
Author : Olga Korosteleva
Publisher : CRC Press
Release : 2022-02-14
ISBN : 1000537374
Language : En, Es, Fr & De

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Book Description :

Stochastic Processes with R: An Introduction cuts through the heavy theory that is present in most courses on random processes and serves as practical guide to simulated trajectories and real-life applications for stochastic processes. The light yet detailed text provides a solid foundation that is an ideal companion for undergraduate statistics students looking to familiarize themselves with stochastic processes before going on to more advanced courses. Key Features Provides complete R codes for all simulations and calculations Substantial scientific or popular applications of each process with occasional statistical analysis Helpful definitions and examples are provided for each process End of chapter exercises cover theoretical applications and practice calculations