Kushner H. Numerical Methods for Stochastic Control...2001 torrent

Textbook in PDF format

Changes in the second edition. The second edition differs from the first in that there is a full development of problems where the variance of the diffusion term and the jump distribution can be controlled. Also, a great deal of new material concerning deterministic problems has been added, including very efficient algorithms for a class of problems of wide current interest. 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 problem formulations and sometimes surprising applications appear regu­ larly. We have chosen forms of the models which cover the great bulk of the formulations 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.
Front Matter.
Introduction.
Review of Continuous Time Models.
Controlled Markov Chains.
Dynamic Programming Equations.
The Markov Chain Approximation Method: Introduction.
Construction of the Approximating Markov Chain.
Computational Methods for Controlled Markov Chains.
The Ergodic Cost Problem: Formulation and Algorithms.
Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations.
Weak Convergence and the Characterization of Processes.
Convergence Proofs.
Convergence for Reflecting Boundaries, Singular Control and Ergodic Cost Problems.
Finite Time Problems and Nonlinear Filtering.
Controlled Variance and Jumps.
Problems from the Calculus of Variations: Finite Time Horizon.
Problems from the Calculus of Variations: Infinite Time Horizon.
The Viscosity Solution Approach to Proving Convergence of Numerical Schemes.
Back Matter