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 Electronic Journal of Probability > Vol. 2 (1997) > Paper 8 open journal systems 


Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations

Gerald Kager, Technische Universität Berlin
Michael Scheutzow, Technische Universität Berlin


Abstract
Let $Z$ be an $R^m$-valued semimartingale with stationary increments which is realized as a helix over a filtered metric dynamical system $S$. Consider a stochastic differential equation with Lipschitz coefficients which is driven by $Z$. We show that its solution semiflow $phi$ has a version for which $varphi(t,omega)=phi(0,t,omega)$ is a cocycle and therefore ($S$,$varphi$) is a random dynamical system. Our results generalize previous results which required $Z$ to be continuous. We also address the case of local Lipschitz coefficients with possible blow-up in finite time. Our abstract perfection theorems are designed to cover also potential applications to infinite dimensional equations.




Full text: PDF

Pages: 1-17

Published on: December 2, 1997
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Electronic Journal of Probability. ISSN: 1083-6489