@article{EJP894,
author = {Georgi Dimitroff and Michael Scheutzow},
title = {Attractors and Expansion for Brownian Flows},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Stochastic flow; stochastic differential equation; attractor; chaining},
abstract = {We show that a stochastic flow which is generated by a stochastic differential equation on $\mathbb{R}^d$ with bounded volatility has a random attractor provided that the drift component in the direction towards the origin is larger than a certain strictly positive constant $\beta$ outside a large ball. Using a similar approach, we provide a lower bound for the linear growth rate of the inner radius of the image of a large ball under a stochastic flow in case the drift component in the direction away from the origin is larger than a certain strictly positive constant $\beta$ outside a large ball. To prove the main result we use chaining techniques in order to control the growth of the diameter of subsets of the state space under the flow.},
pages = {no. 42, 1193-1213},
issn = {1083-6489},
doi = {10.1214/EJP.v16-894},
url = {http://ejp.ejpecp.org/article/view/894}}