Fractional Brownian flows

2008/04/28 by Sreekar Vadlamani, Vadlamani, Sreekar
Economics, Econometrics and Finance · Mathematics · #60G99 #60H10 #60J60 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0804.4376

openalex publication_date 2008/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Flow properties of differential equations driven by fractional Brownian motion
• Stochastic differential equations driven by fractional Brownian motion: dependence on the Hurst parameter
• Existence of a density of the 2Dim Stochastic Navier Stokes Equation driven by Levy processes or fractional Brownian motion
• Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Hypoelliptic Case
• Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case