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Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes

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  • Tang, Linjun
  • Zheng, Shengchao
  • Tan, Zhongquan

Abstract

In this paper, the limit properties of properly time-scaled and normalized maxima of minimum of vector-valued Gaussian processes are studied. It is shown that the maxima of dependent samples of those processes converge weakly on the space of continuous functions to a stochastic process with explicit finite-dimensional distributions.

Suggested Citation

  • Tang, Linjun & Zheng, Shengchao & Tan, Zhongquan, 2021. "Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000997
    DOI: 10.1016/j.spl.2021.109137
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    References listed on IDEAS

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    1. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2014. "On the probability of conjunctions of stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 141-148.
    2. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2015. "Extremes of vector-valued Gaussian processes: Exact asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4039-4065.
    3. Hooghiemstra, G. & Hüsler, J., 1996. "A note on maxima of bivariate random vectors," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 1-6, December.
    4. Das, Bikramjit & Engelke, Sebastian & Hashorva, Enkelejd, 2015. "Extremal behavior of squared Bessel processes attracted by the Brown–Resnick process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 780-796.
    5. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
    6. Krzysztof Dȩbicki & Enkelejd Hashorva & Lanpeng Ji & Chengxiu Ling, 2015. "Extremes of order statistics of stationary processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 229-248, June.
    7. Wang, Yizao, 2018. "Extremes of q-Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2979-3005.
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