Synchronization of Differential Equations Driven by Linear Multiplicative Fractional Brownian Motion

2023/12/09 by Wei Wei, Hui Gao, Wei, Wei +3
Computer Science · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2312.05575

openalex publication_date 2023/12/09 · openalex created_date 2023/12/13 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter H∈((1)/(2),1). We firstly prove that the equation has a unique stationary solution which generates a random dynamical system. Moreover the system has the pathwise singleton sets random attractor. Next we show up the synchronization of solutions of two coupled differential equations. At the end, we discuss two specific situations and provide the corresponding synchronization results.

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