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High excursions for nonstationary generalized chi-square processes

Author

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  • Piterbarg, V. I.

Abstract

Suppose that X(t), t[set membership, variant][0, T], is a centered differentiable Gaussian random process, X1(t), ..., Xn(t) are independent copies of X(t). An exact asymptotic behavior of large deviation probabilities for the process , where b1, b2, ... bn are positive constants is investigated. It is assumed that the variance of the process attains its global maximum in only one inner point of the interval [0, T], with a nondegeneracy condition.

Suggested Citation

  • Piterbarg, V. I., 1994. "High excursions for nonstationary generalized chi-square processes," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 307-337, October.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:2:p:307-337
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    Cited by:

    1. Qiao, Wanli, 2021. "Extremes of locally stationary Gaussian and chi fields on manifolds," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 166-192.
    2. Zhongquan Tan & Changchun Wu, 2014. "Limit laws for the maxima of stationary chi-processes under random index," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 769-786, December.
    3. Tan, Zhongquan & Hashorva, Enkelejd, 2013. "Exact asymptotics and limit theorems for supremum of stationary χ-processes over a random interval," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2983-2998.

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