Hitting probabilities and polar sets for fractional brownian motion

Abstract

Let be the d-dimensional fractional Brownian motion with index . The upper and lower bounds on the hitting probabilities of X(t) are obtained. Sufficient conditions for a compact set to be a polar set for X(t) are proved. It is also proved that if N≤αd, then for any compact set and if N<αd, then for any compact set where B(R^d) denotes the Borel σ-algebra in R^d, and where dim and Dim are HausdorfT dimension and packing dimension respectively

Keywords:

• Fractional Brownian motion
• hitting probability
• polar sets
• Hausdorff dimension
• packing dimension
• AMS Classification Numbers
• Primary: 60G15, 60G17