Controlled Diffusion Processes

  • Nicolai V. Krylov

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

  • Nicolai V. Krylov
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-70913-8
  • Online ISBN 978-3-540-70914-5
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site