Piterbarg Theorems for Chi-processes with Trend

2013/09/01 by Enkelejd Hashorva, Hashorva, Enkelejd, Lanpeng Ji +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1309.0255

22 pages

arxiv created 2013/09/01 · openalex publication_date 2013/09/01 · arxiv updated 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let χ_n(t) = (∑_i=1ⁿ X_i²(t))^1/2,t≥0 be a chi-process with n degrees of freedom where X_i's are independent copies of some generic centered Gaussian process X. This paper derives the exact asymptotic behavior of Psup_t∈[0,T] χ_n(t)>u as u → ∞, where T is a given positive constant, and g(⋅) is some non-negative bounded measurable function. The case g(t)≡0 is investigated in numerous contributions by V.I. Piterbarg. Our novel asymptotic results for both stationary and non-stationary Xare referred to as Piterbarg theorems for chi-processes with trend.

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