Stability equivalence for stochastic differential equations, stochastic differential delay equations and their corresponding Euler-Maruyama methods in $G$-framework
Year: 2024
Type: preprint
Abstract: In this paper, we investigate the stability equivalence problem for stochastic differential delay equations, the auxiliary stochastic differential equations and their corresponding Euler-Maruyama (EM) methods under $G$-framework. More precisely, for $p\geq 2$, we prove the equivalence of practical exponential stability in $p$-th moment sense among stochastic differential delay equations driven by $G$-Brownian motion ($G$-SDDEs), the auxiliary stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs), and their corresponding Euler-Maruyama methods, provided the delay or the step size is small enough. Thus, we can carry out careful simulations to examine the practical exponential stability of the underlying $G$-SDDE or $G$-SDE under some reasonable assumptions.
Source: arXiv (Cornell University)
Author: Lu, Wen
Institution: Yantai University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G4582396152, 由G-布朗运动驱动的几类随机微分方程研究
OpenAlex ID: W4396913719