The multifractal structure of stable occupation measure

[摘要] Let X be a stable subordinator of index alpha and mu be the occupation measure of X. Denote (d) under bar(mu,x) and (d) over bar(mu,x) as the lower and upper local dimensions of mu. We obtain that the Hausdorff dimension of the set of the points where (d) over bar(mu,x) = beta is (2 alpha(2)/beta) - alpha a.s. and the lower bound of packing dimension is 2 alpha - beta a.s. if alpha less than or equal to beta less than or equal to 2 alpha. When beta > 2 alpha, the corresponding set is empty a.s.. And for a.s. omega, the set of the points where (d) over bar(mu,x) = alpha is the closure of X[0, 1].

[发布日期] 1997-03-28