2022-09-292022-09-292021-07-15Caraballo 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-.0219-49371793-6799https://hdl.handle.net/11441/137476This 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.application/pdf36 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/stochastic nonclassical diffusion equationwhite noisefractional Brownian motionwell–posednessill-posednessinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1080/17442508.2022.2028788