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


 
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1. Title Title of document Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations
 
2. Creator Author's name, affiliation, country Gerald Kager; Technische Universität Berlin
 
2. Creator Author's name, affiliation, country Michael Scheutzow; Technische Universität Berlin
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) stochastic differential equation, random dynamical system, cocycle, perfection
 
3. Subject Subject classification 60H10, 28D10, 34C35
 
4. Description 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.

 
 
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7. Date (YYYY-MM-DD) 1997-12-02
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/22
 
10. Identifier Digital Object Identifier 10.1214/EJP.v2-22
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 2
 
12. Language English=en en
 
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