© 1980

Controlled Diffusion Processes


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

About this book


This book deals with the optimal control of solutions of fully observable Itô-type stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved and rules for optimal control strategies are developed.

Topics include optimal stopping; one dimensional controlled diffusion; the Lp-estimates of stochastic integral distributions; the existence theorem for stochastic equations; the Itô formula for functions; and the Bellman principle, equation, and normalized equation.


diffusion diffusion process diffusion process (statistic) fully nonlinear equations linear optimization optimal control stochastic differential equation

Authors and affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • Book Title Controlled Diffusion Processes
  • Authors N. V. Krylov
  • Series Title Stochastic Modelling and Applied Probability
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-70913-8
  • eBook ISBN 978-3-540-70914-5
  • Series ISSN 0172-4568
  • Edition Number 1
  • Number of Pages XII, 310
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by Nauka, Moscow, 1977
  • Topics Systems Theory, Control
    Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


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)