English

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}
}