Article
On stochastic nonclassical diffusion equation with standard and fractional Brownian motion
Author/s | Caraballo Garrido, Tomás
Ngoc, Tran Bao Thach, Tran Ngoc Tuan, Nguyen Huy |
Department | Universidad de Sevilla. Departamento de Ecuaciones diferenciales y Análisis numérico |
Publication Date | 2021-07-15 |
Deposit Date | 2022-09-29 |
Published in |
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Abstract | 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. ... 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. |
Citation | Caraballo Garrido, T., Ngoc, T.B., Thach, T.N. y Tuan, N.H. (2021). On stochastic nonclassical diffusion equation with standard and fractional Brownian motion. Stochastics and Dynamics, 22 (2), 2140011-1-2140011-. |
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