Stochastic Differential Equations and Diffusion Processes

Author: N. Ikeda
Publisher: Elsevier
ISBN: 1483296156
Format: PDF, Kindle
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Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis. A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

Stochastic Processes in Physics and Chemistry

Author: N.G. Van Kampen
Publisher: Elsevier
ISBN: 9780080475363
Format: PDF
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The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004) * Comprehensive coverage of fluctuations and stochastic methods for describing them * A must for students and researchers in applied mathematics, physics and physical chemistry

Stochastic Differential Equations and Applications

Author: Avner Friedman
Publisher: Academic Press
ISBN: 1483217884
Format: PDF, ePub, Docs
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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
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

Statistical Methods for Stochastic Differential Equations

Author: Mathieu Kessler
Publisher: CRC Press
ISBN: 1439849765
Format: PDF
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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.

Large Deviations

Author: Jean-Dominique Deuschel
Publisher: American Mathematical Soc.
ISBN: 082182757X
Format: PDF, Docs
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This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

Theory and Applications of Fractional Differential Equations

Author: Anatoliń≠ Aleksandrovich Kilbas
Publisher: Elsevier
ISBN: 9780444518323
Format: PDF, ePub
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This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Ergodic Control of Diffusion Processes

Author: Ari Arapostathis
Publisher: Cambridge University Press
ISBN: 0521768403
Format: PDF, ePub, Docs
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The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.

Stochastic Differential Equations

Author: Peter H. Baxendale
Publisher: World Scientific
ISBN: 9812770631
Format: PDF, Docs
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This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."