The harmonic mean formula for random processes

2021/06/22 by Krzysztof Bisewski, Enkelejd Hashorva, Bisewski, Krzysztof +3 · 1 citation
Economics, Econometrics and Finance · Decision Sciences · Mathematics · #Stochastic processes and financial applications #Probability and Risk Models #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2106.11707

Abstract

Motivated by the harmonic mean formula in [1], we investigate the relation between the sojourn time and supremum of a random process X(t),t∈ ℝ^d and extend the harmonic mean formula for general stochastically continuous X. We discuss two applications concerning the continuity of distribution of supremum of X and representations of classical Pickands constants.

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• Shift-generated α-homogeneous classes of jointly measurable random fields

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