Event Detail

Event Type: 
Monday, February 25, 2013 - 02:00
Valley Library, Room 1420

Speaker Info

OSU Mathematics

This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Levy’s Brownian motion. We use an integral representation for the covariance function to write Levy’s Brownian motion as an infinite linear combination of independent standard Gaussian random variables and orthogonal polynomials.  Next we introduce a new family of isotropic Gaussian random fields, called the p-processes, of which Levy’s Brownian motion is a special case. Except for Levy’s Brownian motion the p-processes are not locally stationary.  All p-processes also have a representation as an infinite linear combination of independent standard Gaussian random variables.  These expansions of the random fields are used to simulate Levy’s Brownian motion and the p-processes along a ray from the origin using the Cholesky factorization of the covariance matrix.