Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations
Probability
2018-08-23 v2 Analysis of PDEs
Optimization and Control
Abstract
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
Cite
@article{arxiv.1709.00193,
title = {Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations},
author = {Ruoting Gong and Chenchen Mou and Andrzej Swiech},
journal= {arXiv preprint arXiv:1709.00193},
year = {2018}
}
Comments
The title is changed. A reference is added. Several typos are fixed. The proof of Theorem 3.5 is given. An approximated optimal control is discussed. 34 pages