LOCAL ASYMPTOTICS FOR CONTROLLED MARTINGALES

作者：Armstrong Scott N^*; Zeitouni Ofer

来源：Annals of Applied Probability, 2016, 26(3): 1467-1494.

DOI：10.1214/15-AAP1123

• Stochastic control
• martingale
• nonlinear parabolic equation

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.

• 出版日期2016-6