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Fuhrman, Marco; Tessitore, Gianmario

Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces. (English) Zbl 1046.60061

Ann. Probab. 32, No. 1B, 607-660 (2004).
By solving infinite-dimensional forward and backward stochastic differential equations, solutions to a class of semilinear elliptic differential equations on a Hilbert space are studied. The main results are applied to the optimal control for a general nonlinear control system on an infinite time horizon.
Reviewer: Feng-Yu Wang (Beijing)

Cited in 1 Review
Cited in 40 Documents

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

backward stochastic differential equation; partial differential equation; stochastic control
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References:

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