On maxima of chi-processes over threshold dependent grids
Chengxiu Ling, Zhongquan Tan
TL;DR
This paper derives the asymptotic joint distributions of maxima of stationary chi-processes over continuous time and various grids, extending Gaussian case results and analyzing different dependence structures.
Contribution
It extends existing results for Gaussian processes to chi-processes and analyzes maxima over different grid types under various dependence conditions.
Findings
Asymptotic joint distributions derived for chi-process maxima.
Results cover continuous time and discrete grids.
Different dependence structures analyzed with new asymptotic results.
Abstract
In this paper, with motivation from [30] by Piterbarg (Extremes 7:161--177, 2004) and the considerable interest in stationary chi-processes, we derive asymptotic joint distributions of maxima of stationary strongly dependent chi-processes on a continuous time and an uniform grid on the real axis. Our findings extend those for Gaussian cases and give three involved dependence structures via the strongly dependence condition and the sparse, Pickands and dense grids.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Complex Systems and Time Series Analysis · Stochastic processes and financial applications