×

Extremes and local dependence in stationary sequences. (English) Zbl 0506.60030


MSC:

60G10 Stationary stochastic processes
60F99 Limit theorems in probability theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adler, R. J., Weak convergence results for extremal processes generated by dependent random variables, Ann. Probability, 6, 660-667 (1978) · Zbl 0377.60027 · doi:10.1214/aop/1176995486
[2] Berman, S. M., Limiting distribution of the maximum term in a sequence of dependent random variables, Ann. Math. Statist., 33, 894-908 (1962) · Zbl 0109.11804 · doi:10.1214/aoms/1177704458
[3] Chernick, M. R., A limit theorem for the maximum of autoregressive processes with uniform marginal distribution, Ann. Probability, 9, 145-149 (1981) · Zbl 0453.60026 · doi:10.1214/aop/1176994514
[4] Davis, R. A., Ph.D. Thesis (1979), San Diego: University of California, San Diego
[5] Davis, R. A., Limit laws for the maximum and minimum of stationary sequences, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 61, 31-42 (1982) · Zbl 0476.60024 · doi:10.1007/BF00537223
[6] Denzel, G. E.; O’Brien, G. L., Limit theorems for extreme values of chain-dependent processes, Ann. Probability, 3, 773-779 (1975) · Zbl 0322.60088 · doi:10.1214/aop/1176996264
[7] Kallenberg, O., Random measures (1976), Berlin: Berlin, New York: Akademie-Verlag, Berlin: Berlin, New York: Academic Press, Berlin: Berlin, New York: Akademie-Verlag, Berlin: Berlin, New York · Zbl 0345.60032
[8] Leadbetter, M. R., On extreme values in stationary sequences, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 28, 289-303 (1974) · Zbl 0265.60019 · doi:10.1007/BF00532947
[9] Leadbetter, M. R.; Lindgren, G.; Rootzén, H., Extremes and related properties of random sequences and processes, Springer Statistics Series (1983), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0518.60021
[10] Loynes, R. M., Extreme values in uniformly mixing stationary stochastic processes, Ann. Math. Statist., 36, 993-999 (1965) · Zbl 0178.53201 · doi:10.1214/aoms/1177700071
[11] Mori, T., Limit distributions of two-dimensional point processes generated by strong mixing sequences, Yokohama Math. J., 25, 155-168 (1977) · Zbl 0374.60010
[12] Newell, G. F., Asymptotic extremes for m-dependent random variables, Ann. Math. Statist., 35, 1322-1325 (1964) · Zbl 0239.60033 · doi:10.1214/aoms/1177703288
[13] O’Brien, G. L., The maximum term of uniformly mixing stationary processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30, 57-63 (1974) · Zbl 0277.60020 · doi:10.1007/BF00532863
[14] O’Brien, G. L., Limit theorems for the maximum term of a stationary process, Ann. Probability, 2, 540-545 (1974) · Zbl 0286.60018 · doi:10.1214/aop/1176996673
[15] Rootzén, H., Extremes of moving averages of stable processes, Ann. Probability, 6, 847-869 (1978) · Zbl 0394.60025 · doi:10.1214/aop/1176995432
[16] Watson, G. S., Extreme values in samples from m-dependent stationary processes, Ann. Math. Statist., 25, 798-800 (1954) · Zbl 0056.36204 · doi:10.1214/aoms/1177728670
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.