Persistence probabilities of spherical fractional Brownian motion
Probability
2025-03-06 v1 Numerical Analysis
Classical Analysis and ODEs
Numerical Analysis
Abstract
We compute the rate of decay of the persistence probabilities of spherical fractional Brownian motion, which was defined by L\'evy (1965) and Istas (2005). The rate resembles the Euclidean case treated in Molchan (1999). As a by-product we consider the coefficients of series representations of functions with algebraic endpoint singularities in terms of re-scaled Gegenbauer polynomials, which partly generalises Sidi (2009).
Keywords
Cite
@article{arxiv.2503.03425,
title = {Persistence probabilities of spherical fractional Brownian motion},
author = {Frank Aurzada and Max Helmer},
journal= {arXiv preprint arXiv:2503.03425},
year = {2025}
}