2015/01/28 by Robert J. Adler, Adler, Robert, Gennady Samorodnitsky +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F10 Secondary: 60G60 #60G17 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary: 60G15 #Probability (math.PR) #Probability and Statistical Research #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1501.07151
openalex publication_date 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new light in existence of holes. How likely is the field to be above a high level on one compact set (e.g. a sphere) and to be below a fraction of that level on some other compact set, e.g. at the center of the corresponding ball? How likely is the field to be below that fraction of the level \it anywhere inside the ball? We work on the level of large deviations.