Controlled Diffusion Processes (Paperback) (ISBN-13: 9781461260530)

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham 76J). At the same time, Girsanov 25J and Howard 26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier 4J. 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 8J, Mine and Osaki 55J, 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.

Author: N. V. Krylov
ISBN-10: 1461260531
ISBN-13: 9781461260530
Publisher: Springer
Language: English
Published: 10/12/2011
Pages: 308
Format: Paperback
Weight: 1.00lbs
Size: 9.21h x 6.14w x 0.68d