Attractors and Expansion for Brownian Flows

作者：Dimitroff G^*; Scheutzow M

来源：Electronic Journal of Probability, 2011, 16: 1193-1213.

• Stochastic flow
• stochastic differential equation
• attractor
• chaining

We show that a stochastic flow which is generated by a stochastic differential equation on 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.

• 出版日期2011-7-3