This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Lévy's Brownian motion. We use an integral representation for the covariance function to find a new expansion for Lévy'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 Lévy's Brownian motion is a special case. Except for Lévy'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.
We use these expansions of the random fields to simulate Lévy's Brownian motion and the p-processes along a ray from the origin using the Cholesky factorization of the covariance matrix. / Graduation date: 2013
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/37360 |
| Date | 25 February 2013 |
| Creators | Rode, Erica S. |
| Contributors | Ossiander, Mina |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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