Junjie SUN , Zhongquan TAN . THE EXTREMES OF DEPENDENT CHI-PROCESSESATTRACTED BY THE BROWN-RESNICK PROCESS[J]. Acta mathematica scientia, Series B, 2024 , 44(2) : 686 -701 . DOI: 10.1007/s10473-024-0217-9

[1] Albin J M P. On Extremal Theory for Non Differentiable Stationary Processes[D]. Sweden: University of Lund, 1987
[2] Albin J P M. On extremal theory for stationary processes. Ann Probab, 1999, 18: 92-128
[3] Albin J P M, Hashorva E, Ji L, Ling C. Extremes and limit theorems for difference of chi-type processes. ESAIM: Probability and Statistics, 2016, 20: 349-366
[4] Antoch, J, Jarušková, D.Testing for multiple change points. Comput Stat, 2013, 28, 2161-2183
[5] Billingsley P.Convergence of Probability Measures. New York: Wiley, 1999
[6] Brown B M, Resnick S I. Extreme values of independent stochastic processes. J Appl Probab, 1977, 14: 732-739
[7] Buishand T, de Haan L, Zhou C. On spatial extremes: with application to a rainfall problem. Ann Appl Statist, 2008, 2(2): 624-642
[8] Das B, Engelke S, Hashorva E. Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process. Stochastic Process Appl, 2015, 125(2): 780-796
[9] de Haan L, Pereira T. Spatial extremes: models for the stationary case. Ann Stat, 2006, 34(1): 146-168
[10] Eddy W F, Gale J D. The convex hull of a spherically symmetric sample. Adv Appl Probab, 1981, 13: 751-763
[11] Engelke S, Kabluchko Z, Schlather M. An equivalent representation of the Brown-Resnick process. Statist Probab Lett, 2011, 81: 1150-1154
[12] Engelke S, Kabluchko Z, Schlather M. Maxima of independent, non-identically distributed Gaussian vectors. Bernoulli, 2015, 21: 38-61
[13] Engelke S, Malinowski A, Kabluchko Z. Estimation of Hüsler-Reiss distributions and Brown-Resnick processes. J Roy Stat Soc B, 2015, 77(1): 239-265
[14] Frédéric E, Dombry C. Extremes of independent stochastic processes: a point process approach. Extremes, 2016, 19(2): 197-218
[15] Hashorva E. Minima and maxima of elliptical triangular arrays and spherical processes. Bernoulli, 2013, 19: 886-904
[16] Hashorva E, Kabluchko Z, Wübker A. Extremes of independent chi-square random vectors. Extremes, 2012, 15: 35-42
[17] Hashorva E, Ji L. Piterbarg theorems for chi-processes with trend. Extremes, 2015, 18(1): 37-64
[18] Hooghiemstra G, Hüsler J. A note on maxima of bivariate random vectors.Stat Probab Lett, 1996, 31(1): 1-6
[19] Hüsler J, Reiss, R D. Maxima of normal random vectors: Between in-dependence and complete dependence. Stat Probab Lett, 1989, 7(4): 283-286
[20] Jarušková, D. Detecting non-simultaneous changes in means of vectors. TEST, 2015, 24: 681-700
[21] Kabluchko Z,Schlather M, de Haan L. Stationary max-stable fields associated to negative definite functions. Ann Probab, 2009, 37: 2014-2065
[22] Kabluchko Z. Extremes of independent Gaussian processes. Extremes, 2011, 14: 285-310
[23] Leadbetter M R, Lindgren G, Rootzén H.Extremes and Related Properties of Random Sequences and Processes. New York: Springer, 1983
[24] Lindgren G. Extreme values and crossings for the $\chi^{2}$-process and other functions of multidimensional Gaussian proceses with reliability applications. Adv Appl Probab, 1980, 12: 746-774
[25] Lindgren G. Slepian models for $\chi^{2}$-process with dependent components with application to envelope upcrossings. J Appl Probab, 1989, 26: 36-49
[26] Ling C, Tan Z. On maxima of chi-processes over threshold dependent grids. Statistics.2016, 50(3): 579-595
[27] Oesting M, Kabluchko Z, Schlather M. Simulation of Brown-Resnick processes. Extremes, 2012, 15: 89-107
[28] Pickands J. Asymptotic properties of the maximum in a stationary Gaussian process. Trans Amer Math Soc, 1969, 145: 75-86
[29] Piterbarg V I. High extrema of Gaussian chaos processes. Extremes, 2016, 19(2): 253-272
[30] Piterbarg V I.Asymptotic Methods in the Theory of Gaussian Processes and Fields. Providence, RI: Amer Math Soc, 1996
[31] Sharpe K. Some properties of the crossing process generated by a stationary $\chi^{2}$-process. Adv Appl Probab, 1978, 10: 373-391
[32] Tan Z, Hashorva E. Exact asymptotics and limit theorems for supremum of stationary $\chi$-processes over a random interval. Stochastic Process Appl, 2013, 123: 2983-2998
[33] Tan Z, Hashorva E. Limit theorems for extremes of strongly dependent cyclo-stationary $\chi$-processes. Extremes, 2013, 16: 241-254
[34] Tan Z, Wu C. Limit laws for the maxima of stationary chi-processes under random index. Test, 2014, 23: 769-786
[35] Tang L, Zheng S, Tan Z. Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes. Statist Probab Lett, 2021, 176: 109137
[36] Wang Y. Extremes of $q$-Ornstein-Uhlenbeck processes. Stochastic Process Appl, 2018, 128(9): 2979-3005