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The Hausdorff dimensions of the image and the graph of random fields are given under general conditions. The results can be used to a wider class of self-similar random fields and processes, including Brownian motion, Brownian sheet, fractional Brownian motion, processes with stable or (α, β)-fractional stable components. Supported by the National Natural Science Foundation of China  相似文献
2.
In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rd-valued Wiener sheet is (r)=rN-d/2(loglog1/r)d/2 if 2N>d. This solves the problem posed by S. J. Taylor.  相似文献
3.
By constructing proper coupling operators for the integro-differential type Markov generator,we establish the existence of a successful coupling for a class of stochastic differential equations driven by L’evy processes.Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups,and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable L’evy processes.  相似文献
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