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- W2008100172 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." @default.
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- W2008100172 date "1997-01-01" @default.
- W2008100172 modified "2023-09-30" @default.
- W2008100172 title "Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations" @default.
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- W2008100172 doi "https://doi.org/10.1214/ejp.v2-22" @default.
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