Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations
@article{EJP22,
author = {Gerald Kager and Michael Scheutzow},
title = {Generation of One-Sided Random Dynamical Systems by Stochastic Differential Equations},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {2},
year = {1997},
keywords = {stochastic differential equation, random dynamical system, cocycle, perfection},
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.
},
pages = {no. 8, 1-17},
issn = {1083-6489},
doi = {10.1214/EJP.v2-22},
url = {http://ejp.ejpecp.org/article/view/22}}