The Moment Generating Function And Multifractal Analysis For Occupation Measure Of Additive Brownian Motion

Computation of Laplace transforms is an important component of multifrac-tal analysis, and the moment generating function for occupation time of stochastic processes is the Laplace transforms of occupation time. The asymptotic formula of moment generating function for occupation time of transient Brownian motion and symmetric stable process discussed by Dembo and Peres etc. has been used to determine the coarse multifractal spectrum. The additive Brownian motion with many similar properties to Brownian motion is a development generalizaton of Brownian motion in multi-parameter case. Because of the partially-ordered nature in the multi-parameter index space, the problems of additive Brownian motion are much more complex than that of Brownian motion. In this paper, we investigate the occupation time of additive Brownian motion. The main results are as follows:Let B={B(t),t ∈ R₊^N} be N parameter R^d valued additive Brownian motion with d>2N,(I)The asymptotic formula of moment generating function for occupation time For all 0 ≤ θ ≤ θ₀,where {(B₁(t₁),t₁∈ R},…, {B_N(t_N),t_N∈ R} are independent of two-sided Brownian motions.(II)The coarse multifractal analysis for occupation time...