Malliavin Calculus for the stochastic heat equation and results on the density
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909512184627200 |
|---|---|
| author | Farazakis, D. Karali, G. Stavrianidi, A. |
| author_facet | Farazakis, D. Karali, G. Stavrianidi, A. |
| contents | We study the one-dimensional stochastic heat equation with unbounded, nonlinear,Lipschitz coefficients with Dirichlet boundary conditions. Using Malliavin calculus, we construct a piecewise approximation of the solution u and establish regularity results. This approximation enables us to provide a new proof of the existence of a density for the random variable u(t, x) at any fixed t, x. Unlike existing proofs, which rely on comparison principles ([10], [12]), our approach is based purely on a localization argument, which allows us to handle the unbounded coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Malliavin Calculus for the stochastic heat equation and results on the density Farazakis, D. Karali, G. Stavrianidi, A. Analysis of PDEs Probability 60H07 (Primary), 60H15, 35R60 (Secondary) We study the one-dimensional stochastic heat equation with unbounded, nonlinear,Lipschitz coefficients with Dirichlet boundary conditions. Using Malliavin calculus, we construct a piecewise approximation of the solution u and establish regularity results. This approximation enables us to provide a new proof of the existence of a density for the random variable u(t, x) at any fixed t, x. Unlike existing proofs, which rely on comparison principles ([10], [12]), our approach is based purely on a localization argument, which allows us to handle the unbounded coefficients. |
| title | Malliavin Calculus for the stochastic heat equation and results on the density |
| topic | Analysis of PDEs Probability 60H07 (Primary), 60H15, 35R60 (Secondary) |
| url | https://arxiv.org/abs/2410.10115 |