Stochastic Differential Equations

Stochastic Differential Equations
Title Stochastic Differential Equations PDF eBook
Author Bernt Oksendal
Publisher Springer Science & Business Media
Total Pages 218
Release 2013-03-09
Genre Mathematics
ISBN 3662130505

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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.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations
Title Applied Stochastic Differential Equations PDF eBook
Author Simo Särkkä
Publisher Cambridge University Press
Total Pages 327
Release 2019-05-02
Genre Business & Economics
ISBN 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Theory of Stochastic Differential Equations with Jumps and Applications

Theory of Stochastic Differential Equations with Jumps and Applications
Title Theory of Stochastic Differential Equations with Jumps and Applications PDF eBook
Author Rong SITU
Publisher Springer Science & Business Media
Total Pages 444
Release 2006-05-06
Genre Technology & Engineering
ISBN 0387251758

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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.

Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations
Title Numerical Solution of Stochastic Differential Equations PDF eBook
Author Peter E. Kloeden
Publisher Springer Science & Business Media
Total Pages 666
Release 2013-04-17
Genre Mathematics
ISBN 3662126168

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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

Backward Stochastic Differential Equations

Backward Stochastic Differential Equations
Title Backward Stochastic Differential Equations PDF eBook
Author Jianfeng Zhang
Publisher Springer
Total Pages 388
Release 2017-08-22
Genre Mathematics
ISBN 1493972561

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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.

Simulation and Inference for Stochastic Differential Equations

Simulation and Inference for Stochastic Differential Equations
Title Simulation and Inference for Stochastic Differential Equations PDF eBook
Author Stefano M. Iacus
Publisher Springer Science & Business Media
Total Pages 298
Release 2009-04-27
Genre Computers
ISBN 0387758399

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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.

Forward-Backward Stochastic Differential Equations and their Applications

Forward-Backward Stochastic Differential Equations and their Applications
Title Forward-Backward Stochastic Differential Equations and their Applications PDF eBook
Author Jin Ma
Publisher Springer
Total Pages 278
Release 2007-04-24
Genre Mathematics
ISBN 3540488316

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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.