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Volume 4, Issue 3
The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-Field Stochastic Differential Equations

Shang Wu, Jianhua Huang & Feng Chen

DOI: 10.12150/jnma.2022.587

J. Nonl. Mod. Anal., 4 (2022), pp. 587-604.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

Mean-field stochastic differential equations, Tempered fractional Brownian motion, Caputo fractional derivative, Banach fixed point theorem.

  • AMS Subject Headings

60H15, 60H05, 60G22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-587, author = {Wu , ShangHuang , Jianhua and Chen , Feng}, title = {The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-Field Stochastic Differential Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {3}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.587}, url = {http://global-sci.org/intro/article_detail/jnma/20726.html} }
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 -

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.

Wu , ShangHuang , Jianhua and Chen , Feng. (2022). The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-Field Stochastic Differential Equations. Journal of Nonlinear Modeling and Analysis. 4 (3). 587-604. doi:10.12150/jnma.2022.587
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