2021/11/04 by Zahra Aminzare, Aminzare, Zahra
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Electrical engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.PR
paper · pdf · doi:10.48550/arxiv.2111.03155
arxiv created 2021/11/04 · openalex publication_date 2021/11/04 · arxiv updated 2021/11/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of Itô stochastic differential equations (SDEs) with multiplicative noise. We find an upper bound for stochastic logarithmic Lipschitz constants based on known logarithmic norms (matrix measures) of the Jacobian of the drift and diffusion terms of the SDEs. We discuss noise-induced contractivity in SDEs and common noise-induced synchronization in network of SDEs and illustrate the theoretical results on a noisy Van der Pol oscillator. We show that a deterministic Van der Pol oscillator is not contractive. But, adding a multiplicative noise makes the underlying SDE stochastically contractive.