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

Let {X(t), 0⩽t⩽1} be a stochastic process whose range is a random Cantor-like set depending on an α-sequence (0<α<1) and μ is the occupation measure of X(t). In this paper we examine the multifractal structure of μ and obtain the fractal dimensions of the sets of points of where the local dimension of μ is different from α. 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 α, yet the stochastic process under consideration in this work is not even a Markov process.