LOCAL ASYMPTOTICS FOR CONTROLLED MARTINGALES
成果类型：
Article
署名作者：
Armstrong, Scott N.; Zeitouni, Ofer
署名单位：
Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Weizmann Institute of Science; New York University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/15-AAP1123
发表日期：
2016
页码：
1467-1494
关键词：
摘要：
We consider controlled martingales with bounded steps where the controller is allowed at each step to choose the distribution of the next step, and where the goal is to hit a fixed ball at the origin at time n. We show that the algebraic rate of decay (as n increases to infinity) of the value function in the discrete setup coincides with its continuous counterpart, provided a reachability assumption is satisfied. We also study in some detail the uniformly elliptic case and obtain explicit bounds on the rate of decay. This generalizes and improves upon several recent studies of the one dimensional case, and is a discrete analogue of a stochastic control problem recently investigated in Armstrong and Trokhimtchouck.