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Stochastic Differential Equations And Applications

Author: X Mao
Publisher: Elsevier
ISBN: 085709940X
Size: 74.98 MB
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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

Stochastic Differential Equations And Applications

Author: Avner Friedman
Publisher: Academic Press
ISBN: 1483217876
Size: 76.32 MB
Format: PDF, ePub
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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.

Theory Of Stochastic Differential Equations With Jumps And Applications

Author: Rong SITU
Publisher: Springer Science & Business Media
ISBN: 0387251758
Size: 12.57 MB
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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.

Stochastic Differential Equations

Author: Bernt Oksendal
Publisher: Springer Science & Business Media
ISBN: 3662025744
Size: 34.72 MB
Format: PDF, Kindle
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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 And Applications Vii

Author: Giuseppe Da Prato
Publisher: CRC Press
ISBN: 9781420028720
Size: 34.66 MB
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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.

Stochastic Differential Equations

Author: Ludwig Arnold
Publisher: Severn House Paperbacks
ISBN: 9780486482361
Size: 56.22 MB
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Practical and not too rigorous, this highly readable text on stochastic calculus provides an excellent introduction to stochastic partial differential equations. Written at a moderately advanced level, it covers important topics often ignored by other texts on the subject—including Fokker-Planck equations—and it functions as both a classroom text and a reference for professionals and students. The only prerequisite is the mathematical preparation usual for students of physical and engineering sciences. An introductory chapter, intended for reference and review, covers the basics of probability theory. Subsequent chapters focus on Markov and diffusion processes, Wiener process and white noise, and stochastic integrals and differential equations. Additional topics include questions of modeling and approximation, stability of stochastic dynamic systems, optimal filtering of a disturbed signal, and optimal control of stochastic dynamic systems.

Stochastic Differential Equations And Applications

Author: Avner Friedman
Publisher:
ISBN:
Size: 20.72 MB
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This text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. Originally published in 2 volumes, it combines a book of basic theory with a book of applications. Familiarity with elementary probability is the sole prerequisite. 1975 edition.

Stochastic Flows And Stochastic Differential Equations

Author: Hiroshi Kunita
Publisher: Cambridge University Press
ISBN: 9780521599252
Size: 77.35 MB
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Stochastic analysis and stochastic differential equations are rapidly developing fields in probability theory and its applications. This book provides a systematic treatment of stochastic differential equations and stochastic flow of diffeomorphisms and describes the properties of stochastic flows. Professor Kunita's approach regards the stochastic differential equation as a dynamical system driven by a random vector field, including K. Itô's classical theory. Beginning with a discussion of Markov processes, martingales and Brownian motion, Kunita reviews Itô's stochastic analysis. He places emphasis on establishing that the solution defines a flow of diffeomorphisms. This flow property is basic in the modern and comprehensive analysis of the solution and will be applied to solve the first and second order stochastic partial differential equations. This book will be valued by graduate students and researchers in probability. It can also be used as a textbook for advanced probability courses.