Extremes of locally stationary chi-square processes with trend

作者：Liu Peng; Ji Lanpeng^*

来源：Stochastic Processes and Their Applications, 2017, 127(2): 497-525.

DOI：10.1016/j.spa.2016.06.016

• Tail asymptotics
• Chi-square process
• Brownian bridge
• Bessel process
• Fractional Brownian motion
• Generalized Kolmogorov-Dvoretsky-Erdos integral test
• Pickands constant
• Slepian's lemma

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0, 1) of a class of locally stationary chi-square processes with particular admissible trends. An important tool for establishing our results is a weak version of Slepian's lemma for chi-square processes. Some special cases including squared Brownian bridge and Bessel process are discussed.

• 出版日期2017-2