Fractional Brownian flows
Abstract
Description
We consider stochastic flow on n-dimensional Euclidean space driven by fractional Brownian motion with Hurst parameter H greater than half, and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of the ambient n-dimensional Euclidean space, as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Holder norm of the flow.
20 pages, To appear in Journal of Theoretical probability
20 pages, To appear in Journal of Theoretical probability