Malliavin Calculus for rough stochastic differential equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929248200032256 |
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| author | Bugini, Fabio Coghi, Michele Nilssen, Torstein |
| author_facet | Bugini, Fabio Coghi, Michele Nilssen, Torstein |
| contents | In this work we show that rough stochastic differential equations (RSDEs), as introduced by Friz, Hocquet, and Lê (2021), are Malliavin differentiable. We use this to prove existence of a density when the diffusion coefficients satisfies standard ellipticity assumptions. Moreover, when the coefficients are smooth and the diffusion coefficients satisfies a Hörmander condition, the density is shown to be smooth. The key ingredient is to develop a comprehensive theory of linear rough stochastic differential equations, which could be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Malliavin Calculus for rough stochastic differential equations Bugini, Fabio Coghi, Michele Nilssen, Torstein Probability 60H07, 60H10, 60L20 In this work we show that rough stochastic differential equations (RSDEs), as introduced by Friz, Hocquet, and Lê (2021), are Malliavin differentiable. We use this to prove existence of a density when the diffusion coefficients satisfies standard ellipticity assumptions. Moreover, when the coefficients are smooth and the diffusion coefficients satisfies a Hörmander condition, the density is shown to be smooth. The key ingredient is to develop a comprehensive theory of linear rough stochastic differential equations, which could be of independent interest. |
| title | Malliavin Calculus for rough stochastic differential equations |
| topic | Probability 60H07, 60H10, 60L20 |
| url | https://arxiv.org/abs/2402.12056 |