Isotropic Q-fractional Brownian motion on the sphere: regularity and fast simulation

Autor:	Lang, Annika, Müller, Björn
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Numerical Analysis 60H35 33C55 65M70 60G15 60G60 60G17 41A25
Druh dokumentu:	Working Paper
Popis:	As an extension of isotropic Gaussian random fields and Q-Wiener processes on d-dimensional spheres, isotropic Q-fractional Brownian motion is introduced and sample H\"older regularity in space-time is shown depending on the regularity of the spatial covariance operator Q and the Hurst parameter H. The processes are approximated by a spectral method in space for which strong and almost sure convergence are shown. The underlying sample paths of fractional Brownian motion are simulated by circulant embedding or conditionalized random midpoint displacement. Temporal convergence and computational complexity are numerically tested, the latter matching the complexity of simulating a Q-Wiener process if allowing for a temporal error. Comment: 14 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.19649 Zobrazit plný text záznamu View this record from Arxiv