Malliavian differentiablity and smoothness of density for SDES with locally Lipschitz coefficients
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909213166403584 |
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| author | Anton, Cristina |
| author_facet | Anton, Cristina |
| contents | We study Malliavin differentiability for the solutions of a stochastic differential equation with drift of super-linear growth. Assuming we have a monotone drift with polynomial growth, we prove Malliavin differentiability of any order. As a consequence of this result, under the Hörmander's hypothesis we prove that the density of the solution's law with respect to the Lebesgue measure is infinitely differentiable. To avoid non-integrability problems due to the unbounded drift, we follow an approach based on the concepts of Ray Absolute Continuity and Stochastic Gateâux Differentiability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Malliavian differentiablity and smoothness of density for SDES with locally Lipschitz coefficients Anton, Cristina Probability 60H07 (Primary) 60H10, 60H30 (Secondary) We study Malliavin differentiability for the solutions of a stochastic differential equation with drift of super-linear growth. Assuming we have a monotone drift with polynomial growth, we prove Malliavin differentiability of any order. As a consequence of this result, under the Hörmander's hypothesis we prove that the density of the solution's law with respect to the Lebesgue measure is infinitely differentiable. To avoid non-integrability problems due to the unbounded drift, we follow an approach based on the concepts of Ray Absolute Continuity and Stochastic Gateâux Differentiability. |
| title | Malliavian differentiablity and smoothness of density for SDES with locally Lipschitz coefficients |
| topic | Probability 60H07 (Primary) 60H10, 60H30 (Secondary) |
| url | https://arxiv.org/abs/2405.19482 |