2002 Fiscal Year Final Research Report Summary

A reliability system analysis with stochastic differential equation and non-linear DP equation

Research Project

Project/Area Number	13680523
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	社会システム工学
Research Institution	The University of Tokushima
Principal Investigator	OHASHI Mamoru Faculty of Integrated Arts and Sciences Professor, 総合科学部, 教授 (50141924)
Project Period (FY)	2001 – 2002
Keywords	stochastic differential equation / DP equation / reliability system
Research Abstract	1 Purposes of this study are (1) When coefficients of a linear system obey a markov chain, I obtain the stability conditions of the probability linear system. (2) When the probability linear system is stable, I obtain relations with the optimal control policy and viscosity solution of a non-linear DP equation under a suitable criterion. (3) I study algorithms to obtain the solution of a stochastic differential equation. 2 Last year I examined the stability of the linear system with randome parameters obeyed a Markovchain. In particular I studied relations with an exponential function of Martingale and a stochastic differential equation. I adapt this method in analysis of the linear system with random parameters obeyed a Markov chain. This year I studied the Q-learning for Markov decision processes, and presented Research Institute for Mathematical Sciences KOKYUROKU "Mathematical decision making under uncertainty."

(6 results)