Numerical Methods for Stochastic Control Problems in Continuous Time (Applications of Mathematics, Vol 24)

Kushner, Harold Joseph

ISBN 10: 0387978348 / ISBN 13: 9780387978345

Editore: U.S.A.: Springer-Verlag, 1992

Riguardo questo articolo

"The book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks. Convergence of the numerical approximations is proved via the efficient probabilistic methods of weak convergence theory. The methods also apply to the calculation of functionals of uncontrolled processes and for the appropriate to optimal nonlinear filters as well. Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. Essentially all that is required of the approximations are some natural local consistency conditions. The approximations are consistent with standard methods of numerical analysis. The required background in stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques. The book is written on two levels, that of practice (algorithms and applications), and that of the mathematical development. Thus the methods and use should be broadly accessible." (Publisher).

Codice articolo HS41W

Dati bibliografici

• Titolo: Numerical Methods for Stochastic Control Problems in Continuous Time (Applications of Mathematics, Vol 24)
• Editore: U.S.A.: Springer-Verlag
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0387978348
• ISBN 13: 9780387978345
• Rilegatura: Hardcover
• Edizione: 1st Edition
• Condizione: Near Fine
• Condizione della sovraccoperta: No Jacket
• Cataloghi dei venditori:
  • MATHEMATICS & STATISTICS

Descrizione articolo

Riassunto

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" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.

Product Description

Book by Kushner Harold Joseph