Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise

Caibin Zeng; Xiaofang Lin; Jianhua Huang; Qigui Yang

doi:10.3934/cpaa.2020038

Article Contents

2020, Volume 19, Issue 2: 811-834. Doi: 10.3934/cpaa.2020038

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Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise

1.
School of Mathematics, South China University of Technology, Guangzhou 510640, China
2.
College of Science, National University of Defense Technology, Changsha 410073, China

^* Corresponding author
^* Corresponding author

Received: October 31, 2018

Revised: May 31, 2019

Published: October 2019

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Abstract

The fBm-driving rough stochastic lattice dynamical system with a general diffusion term is investigated. First, an area element in space of tensor is desired to define the rough path integral using the Chen-equality and fractional calculus. Under certain conditions, the considered equation is proved to possess a unique local mild path-area solution.

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Mathematics Subject Classification: Primary: 60H15, 60G22; Secondary: 37K60, 37HXX.

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