Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes—Markov processes {X(t), t≥0} with independent self-similar components, that is, X(t) =(X~1(t),…,X~d(t)), where {X~i(t),t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Borel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.