## Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE.(English)Zbl 1333.60150

A Feynman-Kac type representation for Hamilton-Jacobi-Bellman equations by a forward backward stochastic differential equation is provided. For this purpose, a class of BSDEs with partially non-positive jump components is introduced, and the existence of a minimal solution of these BSDEs is obtained by penalization. This is then used for probabilistic representations of fully nonlinear integro-partial differential equations (IPDEs) of Hamilton-Jacobi-Bellman type.

### MSC:

 60H30 Applications of stochastic analysis (to PDEs, etc.) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 35R09 Integro-partial differential equations 60J60 Diffusion processes 60J75 Jump processes (MSC2010) 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 35K55 Nonlinear parabolic equations 93E20 Optimal stochastic control
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### References:

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