EVENT DETAILS AND ABSTRACT

Title: Hausdorff Dimensions of Random Fractals Determined by Levy Processes
Speaker: Jamison Wolf
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Levy processes comprise an important class of continuous time stochastic processes, whose theoretical and application-based popularity spans various disciplines including finance, physics, and telecommunications. To minimize the probabilistic formalism, we will simply regard a Levy process as a family of real-valued random functions that obeys certain minimal requirements. Various sets such as the range, graph, and zero set determined by these random functions typically possess fractal-like properties. Although these sets are random, it has long been known that their Hausdorff dimensions are non-random constants. While numerous results concerning the dimensions of the range and zero set have been published, a characterization of the dimension of the graph has remained an unsolved problem. The overall goal of this lecture is to present a formulation for the computation of the dimension of the graph, and its relationship to the dimensions of the range and zero set.