The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-Field Stochastic Differential Equations
Year: 2022
Author: Shang Wu, Jianhua Huang, Feng Chen
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 3 : pp. 587–604
Abstract
In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.587
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 3 : pp. 587–604
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Mean-field stochastic differential equations Tempered fractional Brownian motion Caputo fractional derivative Banach fixed point theorem.