Abstract
Let X be a symmetric stable process of index αâ (1,2] and let L x t denote the local time at time t and position x. Let V(t) be such that L t V(t) = sup xâ â L t x . We call V(t) the most visited site of X up to time t. We prove the transience of V, that is, lim t ââ |V(t)| = â almost surely. An estimate is given concerning the rate of escape of V. The result extends a well-known theorem of Bass and Griffin for Brownian motion. Our approach is based upon an extension of the RayâKnight theorem for symmetric Markov processes, and relates stable local times to fractional Brownian motion and further to the winding problem for planar Brownian motion.
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