Stochastic Perron for stochastic target games
arXiv:1408.6799 · doi:10.1214/15-AAP1112
Abstract
We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle.
Published at http://dx.doi.org/10.1214/15-AAP1112 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)