Isotropic Q-fractional Brownian motion on the sphere: regularity and fast simulation
Preprint, 2024
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 Hölder 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.
d-dimensional sphere
strong convergence
spherical harmonic functions
Karhunen–Loève expansion
conditionalized random midpoint displacement
FFT
Fractional Brownian motion
spectral methods
circulant embedding
Gaussian processes
Författare
Annika Lang
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Björn Müller
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Time-Evolving Stochastic Manifolds (StochMan)
Europeiska kommissionen (EU) (EC/HE/101088589), 2023-09-01 -- 2028-08-31.
Efficienta approximeringsmetoder för stokastiska fält på mångfalder
Vetenskapsrådet (VR) (2020-04170), 2021-01-01 -- 2024-12-31.
Ämneskategorier (SSIF 2011)
Matematik
Beräkningsmatematik
Geometri
Sannolikhetsteori och statistik
Matematisk analys
DOI
10.48550/arXiv.2410.19649
Relaterade dataset
Code to “Isotropic Q-fractional Brownian motion on the sphere: regularity and fast simulation” [dataset]
DOI: 10.5281/zenodo.14529834