2023 / June Volume 18 No.2
Minimal solution of irregular barrier reflected BDSDEs with left continuous and stochastic linear growth generators
| Published Date |
2023 / June
|
|---|---|
| Title | Minimal solution of irregular barrier reflected BDSDEs with left continuous and stochastic linear growth generators |
| Author | |
| Keyword | |
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| Pagination | 185-224 |
| Abstract | In this paper, we deal with reflected backward doubly stochastic differential equations (RBDSDEs in short) with one rcll reflecting barrier when the coefficient $f$ satisfies a stochastic Lipschitz condition, via penalization method we prove the existence and uniqueness of solutions. The comparison theorem is also established. Via an inf-convolution approximation and comparison theorem, we show the existence of a minimal solution to the RBDSDE under continuous and stochastic linear growth condition, also we provide a minimal solution to RBDSDE with left continuous and stochastic linear growth condition. |
| DOI | |
| AMS Subject Classification |
60H10, 60H05
|
| Received |
2022-12-25
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| Revised |
2023-11-06
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| Accepted |
2023-11-06
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