Approximation of non-stationary fractional Gaussian random fields

Examensarbete för masterexamen

Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12380/300940
Download file(s):
File Description SizeFormat 
Bagmark-Master_s_Thesis.pdf2.54 MBAdobe PDFView/Open
Type: Examensarbete för masterexamen
Title: Approximation of non-stationary fractional Gaussian random fields
Authors: Bågmark, Kasper
Abstract: Numerical approximations of fractional and multifractional Brownian fields are studied by measuring the numerical convergence order. In order to construct these nonstationary fields a study of Gaussian fields, fractal analysis and self-similarity is conducted. The random fields are defined through their covariance function. Simulations are constructed through the Cholesky method, which builds on the Cholesky decomposition of the covariance matrix in order to accurately simulate the nonstationary field. The strong error in L2(; L2(T;R)) is measured for the fractional Brownian motion defined by the fixed Hurst parameter H. It is shown numerically that the convergence rate _ satisfies _ > H for H 2 (0, 0.6). Furthermore the convergence rates are measured for multifractional Brownian motions defined by Hurst functions h : T ! (0, 1) of varying form.
Keywords: Multifractional Brownian motion, non-stationary random fields, Cholesky method, numerical strong convergence rate
Issue Date: 2020
Publisher: Chalmers tekniska högskola / Institutionen för matematiska vetenskaper
URI: https://hdl.handle.net/20.500.12380/300940
Collection:Examensarbeten för masterexamen // Master Theses



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.