Stochastic Differential Equations and Markov Diffusion Processes

  • Wendell Fleming
  • Raymond Rishel
Part of the Applications of Mathematics book series (SMAP, volume 1)


In this chapter we review a part of the theory of continuous parameter stochastic processes which is of interest for the study of Markov models of systems which arise in applications. With one exception the present chapter involves no ideas from control theory, and may be read independently of the rest of the book. (The exception is Theorem 9.2 about the Kalman-Bucy filter; the proof we give depends on the solution to the linear regulator problem.) In the chapter we emphasize material needed to discuss in a mathematically correct way optimal control of diffusion processes in Chap. VI.


Brownian Motion Markov Process Random Vector Stochastic Differential Equation Transition Density 
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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • Wendell Fleming
    • 1
  • Raymond Rishel
    • 2
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA

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