Multifractal analysis of the occupation measures of a kind of stochastic processes

Let {X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a stochastic process whose range is a random Cantor-like set depending on an [alpha]-sequence (0<[alpha]<1) and [mu] is the occupation measure of X(t). In this paper we examine the multifractal structure of [mu] and obtain the fractal dimensions of the sets of points of where the local dimension of [mu] is different from [alpha]. It is interesting to notice that the final results of this paper are identical to those for the occupation measure of a stable subordinator with index [alpha], yet the stochastic process under consideration in this work is not even a Markov process.