Existence Solution for Fractional Mean-Field Backward Stochastic Differential Equation with Stochastic Linear Growth Coefficients

Saouli, Mostapha Abdelouahab

Existence Solution for Fractional Mean-Field Backward Stochastic Differential Equation with Stochastic Linear Growth Coefficients

Files

256-Article Text-768-2-10-20231219.pdf(3.58 MB)

Date

2023-12-31

Authors

Saouli, Mostapha Abdelouahab

Publisher

Institute of Automation and Computer Science, Brno University of Technology

Altmetrics

Abstract

We deal with fractional mean field backwardWe deal with fractional mean field backward stochastic differential equations with hurst parameter $H\in (\frac{1}{2},1)$ when the coefficient $f$ satisfy a stochastic Lipschitz conditions, we prove the existence and uniqueness of solution and provide a comparison theorem. Via an approximation and comparison theorem, we show the existence of a minimal solution when the drift satisfies a stochastic growth condition.

Keywords

Fractional Brownian motion, Backward stochastic differential equations, Stochastic linear growth, Stochastic Lipschitz-continuous, It\^{o}'s fractional formula, Comparison theorem

Citation

Mendel. 2023 vol. 29, č. 2, s. 211-219. ISSN 1803-3814
https://mendel-journal.org/index.php/mendel/article/view/260

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license
http://creativecommons.org/licenses/by-nc-sa/4.0