Limit Theorem for Controlled Backward SDEs and Homogenization of Hamilton-Jacobi-Bellman Equations

Journal Article · Sat Jan 15 04:00:00 EST 2005 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-004-0805-3· OSTI ID:21064220

Buckdahn, Rainer; Ichihara, Naoyuki ^[1]

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1. 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

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTROL THEORY
CONVERGENCE
FUNCTIONS
HAMILTON-JACOBI EQUATIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PROBABILISTIC ESTIMATION
STOCHASTIC PROCESSES