On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion

Tuan, Nguyen Huy and Foondun, Mohammud and Ngoc Thach, Tran and Wang, Renhai (2022) On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion. Bulletin des Sciences Mathématiques, 179. 103158. (https://doi.org/10.1016/j.bulsci.2022.103158)

[thumbnail of Tuan-etal-BSM-2022-On-backward-problems-for-stochastic-fractional-reaction-equations-with-standard]
Preview
 Text. Filename: Tuan_etal_BSM_2022_On_backward_problems_for_stochastic_fractional_reaction_equations_with_standard.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (623kB)| Preview

Abstract

In this work, we study two final value problems for fractional reaction equation with standard Brownian motion W(t) and fractional Brownian motion B H(t), for [Formula presented]. Firstly, the well-posedness of each problem is investigated under strongly choices of data. We aim to find spaces where we obtain the existence of a unique solution of each problem, and establish some regularity results. Next, since the first problem and the second problem when [Formula presented] are ill-posed due to the lack of regularity of the terminal condition, a well-known regularization method called Fourier truncation is applied to construct regularized solutions. Furthermore, convergence results of regularized solutions are proposed.

CORE (COnnecting REpositories)