#### Date of Award

5-2011

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Major

Mathematics

#### Major Professor

Jan Rosinski

#### Committee Members

Xia Chen, Jie Xiong, Mary Leitnaker

#### Abstract

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.

#### Recommended Citation

Turner, Matthew D, "Explicit Lp-norm estimates of infinitely divisible random vectors in Hilbert spaces with applications. " PhD diss., University of Tennessee, 2011.

http://trace.tennessee.edu/utk_graddiss/1035