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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1907.06812 |
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Table of Contents:
- In this article, we mainly study stochastic viscosity solutions for a class of semilinear stochastic integral-partial differential equations (SIPDEs). We investigate a new class of generalized backward doubly stochastic differential equations (GBDSDEs) driven by two independent Brownian motions and an independent Poisson random measure, which involves an integral with respect to a càdlàg increasing process. We first derive existence and uniqueness of the solution of GBDSDEs with general jumps. We then introduce the definition of stochastic viscosity solutions of SIPDEs and give a probabilistic representation for stochastic viscosity solutions of semilinear SIPDEs with nonlinear Neumann boundary conditions. Finally, we establish stochastic maximum principles for the optimal control of a stochastic system modelled by a GBDSDE with general jumps.