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

Let {X(1), 0 less than or equal to t less than or equal to 1} be a stochast ic process whose range is a random Canter-like set depending on an alpha-se quence (0 < alpha < 1) and mu is the occupation measure of X(t). In this pa per we examine the multifractal structure of mu and obtain the fractal dime nsions of the sets of points of where the local dimension of mu is differen t from alpha. It is interesting to notice that the final results of this pa per are identical to those for the occupation measure of a stable subordina tor with index alpha, yet the stochastic process under consideration in thi s work is not even a Markov process. (C) 1999 Elsevier Science B.V. All rig hts reserved.