A note on small probabilities for spherical random fields at a critical regime
Probability
2025-08-13 v1
Abstract
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilities problem. Our results depend on the high-frequency behaviour of the angular power spectrum: the speed of decay of the small ball probability is faster as either the memory parameter or the space-parameter decreases.
Cite
@article{arxiv.2508.08562,
title = {A note on small probabilities for spherical random fields at a critical regime},
author = {Marco Carfagnini},
journal= {arXiv preprint arXiv:2508.08562},
year = {2025}
}