ASYMPTOTIC SUPPORT THEOREM FOR PLANAR ISOTROPIC BROWNIAN FLOWS

作者：Biskamp Moritz^*

来源：Annals of Probability, 2013, 41(2): 699-721.

DOI：10.1214/11-AOP701

• Stochastic flows
• isotropic Brownian flows
• asymptotic expansion
• asymptotic support theorem

It has been shown by various authors that the diameter of a given nontrivial bounded connected set X grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In case of a planar IBF with a positive top-Lyapunov exponent, the precise deterministic linear growth rate K of the diameter is known to exist. In this paper we will extend this result to an asymptotic support theorem for the time-scaled trajectories of a planar IBF phi, which has a positive top-Lyapunov exponent, starting in a nontrivial compact connected set X subset of R-2; that is, we will show convergence in probability of the set of time-scaled trajectories in the Hausdorff distance to the set of Lipschitz continuous functions on [0, 1] starting in 0 with Lipschitz constant K.

• 出版日期2013-3