Thick points for the Cauchy process

الأصل · EN

Let T(x,) denote the occupation measure of an interval of length 2 centered at x by the Cauchy process run until it hits (-∞,-1]∪ [1,∞). We prove that |ₓ|≤ ₁T(x,)/(()²)→ 2/π a.s. as → 0. We also obtain the multifractal spectrum for thick points, i.e. the Hausdorff dimension of the set of α-thick points x for which → 0 T(x,)/(()²) = α> 0.