The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations |
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| Authors: | Shang Wu Jianhua Huang Feng Chen |
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| Institution: | College of Liberal Arts and Science, National University of Defense Technology, Changsha, Hunan 410073, China; School of Science, Changchun University, Changchun, Jilin 130022, China |
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| 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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| Keywords: | Mean-field stochastic differential equations Tempered fractional Brownian motion Caputo fractional derivative Banach fixed point theorem |
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