INDICATOR FRACTIONAL STABLE MOTIONS

Abstract

Using the framework of random walks in random scenery, Cohen and Samorodnitsky ( 2006) introduced a family of symmetric alpha-stable motions called local time fractional stable motions. When alpha = 2, these processes are precisely fractional Brownian motions with 1/2 < H < 1. Motivated by random walks in alternating scenery, we find a complementary family of symmetric alpha-stable motions which we call indicator fractional stable motions. These processes are complementary to local time fractional stable motions in that when alpha = 2, one gets fractional Brownian motions with 0 < H < 1/2.