REMARK ON LOCALLY CONSTANT SELF-SIMILAR PROCESSES

摘要

Let X = {X(t), t ∈ R_+} be a self-similar process with index α > 0. We show that if X is locally constant and P{X(1) = 0} = 0, then the law of X(t) is absolutely continuous. We discuss applications of this result to homogeneous functionals of a multidimensional fractional Brownian motion.