On stochastic nonclassical diffusion equation with standard and fractional Brownian motion
This paper is concerned with the mathematical analysis of terminal value problems for a stochastic non-classical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions. Our two problems are to study in the sense of well-posedness and ill-posedness m...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/137476 |
| Acesso em linha: | https://hdl.handle.net/11441/137476 https://doi.org/10.1080/17442508.2022.2028788 |
| Access Level: | Acceso aberto |
| Palavra-chave: | stochastic nonclassical diffusion equation white noise fractional Brownian motion well–posedness ill-posedness |
| Resumo: | This paper is concerned with the mathematical analysis of terminal value problems for a stochastic non-classical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions. Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a terminal value problem is a problem of determining the statistical properties of the initial data from the final time data. In the case 0 < β ≤ 1, where β is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-poseness results for the problems when β > 1. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fractional Brownian motion. |
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