2 1 Se p 20 09 Attractors and Expansion for Brownian Flows
نویسنده
چکیده
We show that a stochastic flow which is generated by a stochastic differential equation on R 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 β 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 β 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.
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