TY - JOUR
T1 - The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-Field Stochastic Differential Equations
AU - Wu , Shang
AU - Huang , Jianhua
AU - Chen , Feng
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 587
EP - 604
PY - 2022
DA - 2022/06
SN - 4
DO - http://doi.org/10.12150/jnma.2022.587
UR - https://global-sci.org/intro/article_detail/jnma/20726.html
KW - Mean-field stochastic differential equations, Tempered fractional
Brownian motion, Caputo fractional derivative, Banach fixed point theorem.
AB - <p style="text-align: justify;">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.</p>