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Titlebook: Numerical Methods for Stochastic Control Problems in Continuous Time; Harold J. Kushner,Paul G. Dupuis Book 19921st edition Springer-Verla

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书目名称Numerical Methods for Stochastic Control Problems in Continuous Time
编辑Harold J. Kushner,Paul G. Dupuis
视频video
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Numerical Methods for Stochastic Control Problems in Continuous Time;  Harold J. Kushner,Paul G. Dupuis Book 19921st edition Springer-Verla
描述This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob­ lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for­ mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin­ uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift"
出版日期Book 19921st edition
关键词Markov chain; Variation; algorithms; numerical analysis; stochastic processes
版次1
doihttps://doi.org/10.1007/978-1-4684-0441-8
isbn_ebook978-1-4684-0441-8Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer-Verlag New York, Inc. 1992
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Controlled Markov Chains,n controlled finite state Markov chains. In this chapter, we will define some of the canonical control problems for the Markov chain models which will be used in the sequel as “approximating processes.” The cost functions will be defined. The functional equations which are satisfied by these cost fu
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The Markov Chain Approximation Method: Introduction,f functionals of the stochastic processes of interest, of the type described in Chapters 3, 7, 8, 9, 12, and 13. It was shown in Chapter 3 that the cost or optimal cost functionals can be the (at least formal) solutions to certain nonlinear partial differential equations. It is tempting to try to so
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Computational Methods for Controlled Markov Chains,d value function for the approximating Markov chain models. We concentrate on methods for problems which are of interest over a potentially unbounded time interval. Numerical methods for the ergodic problem will be discussed in Chapter 7, and are simple modifications of the ideas of this chapter. So
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The Ergodic Cost Problem: Formulation and Algorithms, useful to discuss the appropriate dynamic programming equations and some additional background material. The natural state spaces for control problems that are of interest over a long time interval are often unbounded, and they must be truncated for numerical purposes. One standard way of doing thi
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Convergence Proofs, discounted problems with absorbing boundaries; diffusion and jump diffusion models; optimal stopping problems, and problems where we stop on hitting a target set and where there is no discounting. The convergence results for the case of reflecting boundaries and the singular and ergodic control pro
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