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Controlled Diffusion Processes

  • Book
  • © 1980

Overview

Authors:
  1. Nicolai V. Krylov

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 14)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction to the Theory of Controlled Diffusion Processes

    Pages 1-43

  3. Auxiliary Propositions

    Pages 45-128

  4. General Properties of a Payoff Function

    Pages 129-161

  5. The Bellman Equation

    Pages 163-211

  6. The Construction of ε-Optimal Strategies

    Pages 213-243

  7. Controlled Processes with Unbounded Coefficients: The Normed Bellman Equation

    Pages 245-292

  8. Back Matter

    Pages 293-308
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Keywords

About this book

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.

Reviews

From the reviews:

“The book treats a large class of fully nonlinear parabolic PDEs via probabilistic methods. … The monograph may be strongly recommended as an excellent reading to PhD students, postdocs et al working in the area of controlled stochastic processes and/or nonlinear partial differential equations of the second order. … recommended to a wider audience of all students specializing in stochastic analysis or stochastic finance starting from MSc level.” (Alexander Yu Veretennikov, Zentralblatt MATH, Vol. 1171, 2009)

Authors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Nicolai V. Krylov

Bibliographic Information

  • Book Title: Controlled Diffusion Processes

  • Authors: Nicolai V. Krylov

  • Series Title: Stochastic Modelling and Applied Probability

  • DOI: https://doi.org/10.1007/978-3-540-70914-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1980

  • Softcover ISBN: 978-3-540-70913-8Published: 15 October 2008

  • eBook ISBN: 978-3-540-70914-5Published: 26 September 2008

  • Series ISSN: 0172-4568

  • Series E-ISSN: 2197-439X

  • Edition Number: 1

  • Number of Pages: XII, 310

  • Additional Information: Original Russian edition published by Nauka, Moscow, 1977

  • Topics: Systems Theory, Control, Probability Theory and Stochastic Processes

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