Author:
Swishchuk Anatoliy,Limnios Nikolaos
Abstract
In this paper, we introduced controlled discrete-time semi-Markov random evolutions. These processes are random evolutions of discrete-time semi-Markov processes where we consider a control. applied to the values of random evolution. The main results concern time-rescaled weak convergence limit theorems in a Banach space of the above stochastic systems as averaging and diffusion approximation. The applications are given to the controlled additive functionals, controlled geometric Markov renewal processes, and controlled dynamical systems. We provide dynamical principles for discrete-time dynamical systems such as controlled additive functionals and controlled geometric Markov renewal processes. We also produce dynamic programming equations (Hamilton–Jacobi–Bellman equations) for the limiting processes in diffusion approximation such as controlled additive functionals, controlled geometric Markov renewal processes and controlled dynamical systems. As an example, we consider the solution of portfolio optimization problem by Merton for the limiting controlled geometric Markov renewal processes in diffusion approximation scheme. The rates of convergence in the limit theorems are also presented.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference50 articles.
1. RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
2. Random evolutions: A survey of results and problems
3. Stochastic Systems in Merging Phase Space;Koroliuk,2005
4. Evolution of System in Random Media;Korolyuk,1995
5. Evolution of Biological Systems in Random Media: Limit Theorems and Stability;Swishchuk,2003
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