Local asymptotics for controlled martingales - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2016

Local asymptotics for controlled martingales

Résumé

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.

Dates et versions

hal-01483474 , version 1 (06-03-2017)

Identifiants

Citer

Scott N. Armstrong, Ofer Zeitouni. Local asymptotics for controlled martingales. The Annals of Applied Probability, 2016, 26 (3), pp.1467-1494. ⟨10.1214/15-AAP1123⟩. ⟨hal-01483474⟩
113 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More