Approximation of non-stationary fractional Gaussian random fields
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2020
Författare
Bågmark, Kasper
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Multifractional Brownian motion, non-stationary random fields, Cholesky method, numerical strong convergence rate