Taylor expansion of the density in a stochastic heat equation
We prove a general result on asymptotic expansions of densities for families of perturbed Wiener functionals. As an application, we consider a stochastic heat equation driven by a space-time white noise εW˙ t,x, ε ∈ (0, 1]. The main theorem describes the asymptotics, as ε ↓ 0, of the density pε t,x(...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 1998 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/16907 |
| Online Access: | https://hdl.handle.net/2445/16907 |
| Access Level: | Open access |
| Keyword: | Equacions integrals estocàstiques Càlcul de Malliavin Stochastic differential equations Malliavin calculus |
| Summary: | We prove a general result on asymptotic expansions of densities for families of perturbed Wiener functionals. As an application, we consider a stochastic heat equation driven by a space-time white noise εW˙ t,x, ε ∈ (0, 1]. The main theorem describes the asymptotics, as ε ↓ 0, of the density pε t,x(y) of the solution at a fixed point (t, x) for some particular value y ∈ R, which, in the diffusion case, plays the role of the diagonal. |
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