On terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motions
In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard Brownian motion and fractional Brownian motion with Hurst parameter h ∈ ( 1/2 , 1) separately. For each problem, we provide a representation for the mild solution and find the space...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/130372 |
| Acceso en línea: | https://hdl.handle.net/11441/130372 https://doi.org/10.3233/ASY-201637 |
| Access Level: | acceso abierto |
| Palabra clave: | Bi-parabolic equation Standard Brownian motion Fractional Brownian motion Terminal value problem Illposedness |
| Sumario: | In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard Brownian motion and fractional Brownian motion with Hurst parameter h ∈ ( 1/2 , 1) separately. For each problem, we provide a representation for the mild solution and find the space where the existence of the solution is guaranteed. Additionally, we show clearly that the solution of each problem is not stable, which leads to the ill-posedness of each problem. Finally, we propose two regularization results for both considered problems by using the filter regularization method. |
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