Abstract
The main goal of this paper is to study the sample path properties for the harmonisabletype N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an (N, d)-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
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