Local asymptotics for controlled martingales
Armstrong, Scott N.; Zeitouni, Ofer (2016), Local asymptotics for controlled martingales, The Annals of Applied Probability, 26, 3, p. 1467-1494. 10.1214/15-AAP1123
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1402.2402v2
Journal nameThe Annals of Applied Probability
Institute of Mathematical Statistics
MetadataShow full item record
Abstract (EN)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 [Calc. Var. Partial Differential Equations 38 (2010) 521–540].
Subjects / KeywordsStochastic control; Martingale; Nonlinear parabolic equation.
Showing items related by title and author.
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations Armstrong, Scott N.; Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2014) Article accepté pour publication ou publié