LOWER TAILS OF SELF-SIMILAR STABLE PROCESSES

For a self-similar alpha-stable process with stationary increments {X( t), 0 less than or equal to t less than or equal to 1} we study the as ymptotic behaviour of the probability that the process stays within th e interval [-epsilon, epsilon], as epsilon becomes small. This behavio ur turns out to be only partially determined by the index of stability alpha and parameter of self-similarity H. 1350-7265 (C) 1998 Chapman & Hall.