On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913710510964736 |
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| author | Belfadli, Rachid Boulanba, Lahcen Ouknine, Youssef |
| author_facet | Belfadli, Rachid Boulanba, Lahcen Ouknine, Youssef |
| contents | In this paper, we establish Malliavin differentiability and absolute continuity for $α, β$-doubly perturbed diffusion process with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Furthermore, under some regularity conditions on the coefficients, we prove that the solution $X_t$ has a smooth density for all $t\in(0, t_0)$ for some finite number $t_0>0$. Our results recover earlier works by Yue and Zhang (2015) and Xue, Yue and Zhang (2016), and the proofs are based on the techniques of the Malliavin calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes Belfadli, Rachid Boulanba, Lahcen Ouknine, Youssef Probability 60H07, 60H10 In this paper, we establish Malliavin differentiability and absolute continuity for $α, β$-doubly perturbed diffusion process with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Furthermore, under some regularity conditions on the coefficients, we prove that the solution $X_t$ has a smooth density for all $t\in(0, t_0)$ for some finite number $t_0>0$. Our results recover earlier works by Yue and Zhang (2015) and Xue, Yue and Zhang (2016), and the proofs are based on the techniques of the Malliavin calculus. |
| title | On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes |
| topic | Probability 60H07, 60H10 |
| url | https://arxiv.org/abs/2502.19999 |