Limit Theorem for Controlled Backward SDEs and Homogenization of Hamilton-Jacobi-Bellman Equations
- Departement de Mathematiques, Universite de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, B.P. 809, 29285 Brest Cedex (France)
We prove a convergence theorem for a family of value functions associated with stochastic control problems whose cost functions are defined by backward stochastic differential equations. The limit function is characterized as a viscosity solution to a fully nonlinear partial differential equation of second order. The key assumption we use in our approach is shown to be a necessary and sufficient assumption for the homogenizability of the control problem. The results generalize partially homogenization problems for Hamilton-Jacobi-Bellman equations treated recently by Alvarez and Bardi by viscosity solution methods. In contrast to their approach, we use mainly probabilistic arguments, and discuss a stochastic control interpretation for the limit equation.
- OSTI ID:
- 21064220
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 51; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
Similar Records
On an asymptotic viscosity solution property of solutions of discrete Hamilton–Jacobi–Bellman equations
On Nonuniqueness of Solutions of Hamilton–Jacobi–Bellman Equations