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

Nguyen Huy Tuan, Mohammud Foondun, Tran Ngoc Thach, Renhai Wang

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
41 Downloads (Pure)

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.

Original languageEnglish
Article number103158
JournalBulletin des Sciences Mathématiques
Volume179
Early online date3 Jun 2022
DOIs
Publication statusPublished - 1 Oct 2022

Keywords

  • Fractional Brownian motion
  • Fractional differential equation
  • Fractional reaction equation
  • Ill-posedness
  • Inverse problem
  • Well–posedness

Fingerprint

Dive into the research topics of 'On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion'. Together they form a unique fingerprint.

Cite this