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Controlled Diffusion Processes (Paperback, 1st ed. 1980. 2nd printing 2008)
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Controlled Diffusion Processes (Paperback, 1st ed. 1980. 2nd printing 2008)
Series: Stochastic Modelling and Applied Probability, 14
Expected to ship within 10 - 15 working days
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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.
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