I give explicit estimates of the Lp-norm of a mean zero infinitely divisible random vector taking values in a Hilbert space in terms of a certain mixture of the L2- and Lp-norms of the Levy measure. Using decoupling inequalities, the stochastic integral driven by an infinitely divisible random measure is defined. As a first application utilizing the Lp-norm estimates, computation of Ito Isomorphisms for different types of stochastic integrals are given. As a second application, I consider the discrete time signal-observation model in the presence of an alpha-stable noise environment. Formulation is given to compute the optimal linear estimate of the system state.
Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-2115 |
Date | 01 May 2011 |
Creators | Turner, Matthew D |
Publisher | Trace: Tennessee Research and Creative Exchange |
Source Sets | University of Tennessee Libraries |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Doctoral Dissertations |
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