Extremes and Limit Theorems for Difference of Chi-type processes

2015/08/11 by P. Albin, J.M.P. Albin, Enkelejd Hashorva +9
Decision Sciences · Mathematics · #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1508.02758

To appear in ESAIM P&S

openalex publication_date 2015/08/11 · arxiv created 2016/07/15 · arxiv updated 2016/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let \ζ_m,k^(κ)(t), t ≥0\, κ>0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In applications such as physical sciences and engineering dealing with structure reliability, of interest is the approximation of the probability that the random process ζ_m,k^(κ) stays in some safety region up to a fixed time T. In this paper we derive the asymptotics of ℙ\sup_{t∈[0, T]}ζ_m,k^(κ)(t)> u\, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.

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