# stochastic differential equations an introduction with applications universitext

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## Stochastic Differential Equations

**Author :**Bernt Øksendal

**ISBN :**9783642143946

**Genre :**Mathematics

**File Size :**87. 42 MB

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## Stochastic Differential Equations

**Author :**Bernt Oksendal

**ISBN :**9783662130506

**Genre :**Mathematics

**File Size :**75. 86 MB

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These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

## Stochastic Differential Equations

**Author :**Bernt Oksendal

**ISBN :**9783662025741

**Genre :**Mathematics

**File Size :**33. 23 MB

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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 Partial Differential Equations

**Author :**H. Holden

**ISBN :**9781468492156

**Genre :**Mathematics

**File Size :**21. 54 MB

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This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.

## Stochastic Differential Equations And Applications

**Author :**Avner Friedman

**ISBN :**9781483217888

**Genre :**Mathematics

**File Size :**87. 17 MB

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Stochastic Differential Equations and Applications, Volume 2 is an eight-chapter text that focuses on the practical aspects of stochastic differential equations. This volume begins with a presentation of the auxiliary results in partial differential equations that are needed in the sequel. The succeeding chapters describe the behavior of the sample paths of solutions of stochastic differential equations. These topics are followed by a consideration of an issue whether the paths can hit a given set with positive probability, as well as the stability of paths about a given manifold and with spiraling of paths about this manifold. Other chapters deal with the applications to partial equations, specifically with the Dirichlet problem for degenerate elliptic equations. These chapters also explore the questions of singular perturbations and the existence of fundamental solutions for degenerate parabolic equations. The final chapters discuss stopping time problems, stochastic games, and stochastic differential games. This book is intended primarily to undergraduate and graduate mathematics students.

## Numerical Solution Of Stochastic Differential Equations

**Author :**Peter E. Kloeden

**ISBN :**9783662126165

**Genre :**Mathematics

**File Size :**70. 41 MB

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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

**Author :**Lawrence C. Evans

**ISBN :**9781470410544

**Genre :**Mathematics

**File Size :**71. 63 MB

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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).

## Simulation And Inference For Stochastic Differential Equations

**Author :**Stefano M. Iacus

**ISBN :**0387758399

**Genre :**Computers

**File Size :**59. 22 MB

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This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.

## From Elementary Probability To Stochastic Differential Equations With Maple

**Author :**Sasha Cyganowski

**ISBN :**9783642561443

**Genre :**Mathematics

**File Size :**25. 16 MB

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This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.

## Applied Stochastic Control Of Jump Diffusions

**Author :**Bernt Øksendal

**ISBN :**9783540698265

**Genre :**Mathematics

**File Size :**61. 15 MB

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.