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Long time asymptotics for fully nonlinear Bellman equations: a Backward SDE approach

Abstract : We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control both on drift and diffusion coefficients. We prove that, as time horizon goes to infinity, the long run average solution is characterized by a nonlinear ergodic equation. Our results hold under dissipativity conditions, and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments relying on new backward SDE representation for nonlinear parabolic, elliptic and ergodic equations.
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https://hal.archives-ouvertes.fr/hal-01071396
Contributor : Huyên Pham <>
Submitted on : Saturday, October 4, 2014 - 1:59:00 PM
Last modification on : Friday, March 27, 2020 - 3:12:44 AM
Document(s) archivé(s) le : Monday, January 5, 2015 - 1:31:09 PM

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Andrea Cosso, Marco Fuhrman, Huyen Pham. Long time asymptotics for fully nonlinear Bellman equations: a Backward SDE approach. Stochastic Processes and their Applications, Elsevier, 2016, 126 (7), pp.1932-1973. ⟨10.1016/j.spa.2015.12.009⟩. ⟨hal-01071396⟩

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