Titlebook: Controlled Diffusion Processes; Nicolai V. Krylov Book 1980 Springer-Verlag Berlin Heidelberg 1980 diffusion.diffusion process.diffusion p

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Book 1980aki [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

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0172-4568 pment 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 equation978-3-540-70913-8978-3-540-70914-5Series ISSN 0172-4568 Series E-ISSN 2197-439X

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Controlled Processes with Unbounded Coefficients: The Normed Bellman Equation,.(.,.), and .(.,.) are bounded functions of . for each (.,.). The objective of Chapter 6 is to carry the results obtained in Chapters 3–5 over to controlled processes with coefficients unbounded with respect to ., and also to consider controlled processes on an infinite time interval.

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Auxiliary Propositions,an interval of time; the points on this interval are, as a rule, denoted by ., .... denotes an open set in Euclidean space, . the closure of ., and . the boundary of .... denotes an open set in .; the points of . are expressed as (.,.) where .∈., .∈.. .′. denotes the parabolic boundary of . (see Section 4.5).

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Controlled Processes with Unbounded Coefficients: The Normed Bellman Equation,.(.,.), and .(.,.) are bounded functions of . for each (.,.). The objective of Chapter 6 is to carry the results obtained in Chapters 3–5 over to controlled processes with coefficients unbounded with respect to ., and also to consider controlled processes on an infinite time interval.