Consider a centred random walk in dimension one with a positive finite variance σ2, and let τB be the hitting time for a bounded Borel set B with a non-empty interior. We prove the asymptotic Px(τBn)∼2/πσ−1VB(x)n−1/2 and provide an explicit formula for the limit VB as a function of...

The aim of this paper is to show, using some of Barnsley's ideas, how it is possible to generalize a fractal interpolation problem to certain post critically finite (PCF) compact sets in ℝn. We use harmonic functions to solve this fractal interpolation problem.

We prove regularity estimates for functions which are harmonic with respect to certain jump processes. The aim of this article is to extend the method of Bass–Levin (2002) [3] and Bogdan–Sztonyk (2005) [6] to more general processes. Furthermore, we establish a new version of the Harnack...

In this paper we study a subordinate Brownian motion with a Gaussian component and a rather general discontinuous part. The assumption on the subordinator is that its Laplace exponent is a complete Bernstein function with a Lévy density satisfying a certain growth condition near zero. The main...