Stochastic Differential Equations and Diffusion Processes

Author: N. Ikeda
Publisher: Elsevier
ISBN: 1483296156
Format: PDF, Mobi
Download Now
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.

Ergodic Control of Diffusion Processes

Author: Ari Arapostathis
Publisher: Cambridge University Press
ISBN: 0521768403
Format: PDF, Kindle
Download Now
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
Download Now
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."

Controlled Diffusion Processes

Author: N. V. Krylov
Publisher: Springer Science & Business Media
ISBN: 3540709142
Format: PDF, ePub, Docs
Download Now
Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Partial Differential Equations of Parabolic Type

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486318265
Format: PDF, ePub, Docs
Download Now
With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Stochastic Differential Equations and Applications

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486141128
Format: PDF, ePub
Download Now
Originally published in 2 volumes, this text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. 1975 edition.

Stochastic Processes in Physics and Chemistry

Author: N.G. Van Kampen
Publisher: Elsevier
ISBN: 9780080475363
Format: PDF, Kindle
Download Now
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

Diffusion processes and partial differential equations

Author: Kazuaki Taira
Publisher: Academic Pr
ISBN:
Format: PDF, ePub, Mobi
Download Now
This book provides a careful and accessible exposition of functional analytic methods in stochastic analysis. It focuses on the relationship between Markov processes and elliptic boundary value problems and explores several recent developments in the theory of partial differential equations which have made further progress in the study of Markov processes possible. This book will have great appeal to both advanced students and researchers as an introduction to three interrelated subjects in analysis (Markov processes, semigroups, and elliptic boundary value problems), providing powerful methods for future research.

Generalized Diffusion Processes

Author: Nikola_ Ivanovich Portenko
Publisher: American Mathematical Soc.
ISBN: 9780821898260
Format: PDF, ePub, Mobi
Download Now
Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.