Stability equivalence for stochastic differential equations, stochastic differential delay equations and their corresponding Euler-Maruyama methods in $G$-framework

Wen Lu

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arXiv · 2405.07519

Stability equivalence for stochastic differential equations, stochastic differential delay equations and their corresponding Euler-Maruyama methods in $G$-framework

Wen Lu

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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.

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Wen Lu. 2024-05-13. Stability equivalence for stochastic differential equations, stochastic differential delay equations and their corresponding Euler-Maruyama methods in $G$-framework. https://arxiv.org/abs/2405.07519

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