Solution of the Stochastic control problem in unbounded domains

✍ Scribed by Prentiss Robinson; John Moore

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 541 KB
• Volume: 295
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(73)90163-4

✦ Synopsis

Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the &ocha&ic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more eficient than existing methods of solution.