Stochastic Differential Equations

Author: Bernt Oksendal
Publisher: Springer Science & Business Media
ISBN: 3662130505
Format: PDF, Docs
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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
Publisher: Springer Science & Business Media
ISBN: 3662025744
Format: PDF, ePub
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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

Numerical Solution of Stochastic Differential Equations

Author: Peter E. Kloeden
Publisher: Springer Science & Business Media
ISBN: 3662126168
Format: PDF, ePub, Docs
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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

Stochastic Differential Equations and Applications

Author: X Mao
Publisher: Elsevier
ISBN: 085709940X
Format: PDF
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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

Statistical Methods for Stochastic Differential Equations

Author: Mathieu Kessler
Publisher: CRC Press
ISBN: 1439849765
Format: PDF, Docs
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The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.

An Introduction to Stochastic Differential Equations

Author: Lawrence C. Evans
Publisher: American Mathematical Soc.
ISBN: 1470410540
Format: PDF, ePub
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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).

Stochastic Differential Equations with Markovian Switching

Author: Xuerong Mao
Publisher: Imperial College Press
ISBN: 1860947018
Format: PDF
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This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.

Stochastic Differential Equations

Author: Michael J. Panik
Publisher: John Wiley & Sons
ISBN: 1119377382
Format: PDF
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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

Author: N El Karoui
Publisher: CRC Press
ISBN: 9780582307339
Format: PDF, ePub
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This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.