On mixed fractional SDEs with discontinuous drift coefficient
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913297873240064 |
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| author | Sönmez, Ercan |
| author_facet | Sönmez, Ercan |
| contents | We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_14176 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On mixed fractional SDEs with discontinuous drift coefficient Sönmez, Ercan Probability We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient. |
| title | On mixed fractional SDEs with discontinuous drift coefficient |
| topic | Probability |
| url | https://arxiv.org/abs/2010.14176 |