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| Format: | Preprint |
| Published: |
2019
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| Online Access: | https://arxiv.org/abs/1907.06812 |
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| _version_ | 1866914838059417600 |
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| author | Wu, Jinbiao |
| author_facet | Wu, Jinbiao |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_06812 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stochastic viscosity solutions for stochastic integral-partial differential equations and singular stochastic control Wu, Jinbiao Probability Analysis of PDEs 60H15, 60H10, 93E20 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. |
| title | Stochastic viscosity solutions for stochastic integral-partial differential equations and singular stochastic control |
| topic | Probability Analysis of PDEs 60H15, 60H10, 93E20 |
| url | https://arxiv.org/abs/1907.06812 |