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- Title
Piterbarg theorems for chi-processes with trend.
- Authors
Hashorva, Enkelejd; Ji, Lanpeng
- Abstract
Let $\chi _{n}(t) = ({\sum }_{i=1}^{n} {X_{i}^{2}}(t))^{1/2},\ {t\ge 0}$ be a chi-process with n degrees of freedom where X's are independent copies of some generic centered Gaussian process X. This paper derives the exact asymptotic behaviour of where T is a given positive constant, and g(⋅) is some non-negative bounded measurable function. The case g( t)≡0 has been investigated in numerous contributions by V.I. Piterbarg. Our novel asymptotic results, for both stationary and non-stationary X, are referred to as Piterbarg theorems for chi-processes with trend.
- Subjects
GAUSSIAN processes; ASYMPTOTIC distribution; INTEGRAL theorems; FUNCTIONS of bounded variation; BOUNDED arithmetics
- Publication
Extremes, 2015, Vol 18, Issue 1, p37
- ISSN
1386-1999
- Publication type
Article
- DOI
10.1007/s10687-014-0201-1