×

Upcrossing probabilities for stationary Gaussian processes. (English) Zbl 0206.18802


MSC:

60G15 Gaussian processes
60G10 Stationary stochastic processes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. W. Anderson, An introduction to multivariate statistical analysis, Wiley Publications in Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. · Zbl 0083.14601
[2] Yu. K. Belyaev, Continuity and Hölder’s conditions for sample functions of stationary Gaussian processes, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 23 – 33.
[3] Simeon M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35 (1964), 502 – 516. · Zbl 0122.13503 · doi:10.1214/aoms/1177703551
[4] H. Cramér, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J., 1951.
[5] Harald Cramér, On the intersections between the trajectories of a normal stationary stochastic process and a high level, Ark. Mat. 6 (1966), 337 – 349 (1966). · Zbl 0144.39703 · doi:10.1007/BF02590962
[6] H. Cramér and M. R. Leadbetter, Stationary and related stochastic processes; sample function properties and their applications, Wiley, New York, 1955.
[7] B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. · Zbl 0056.36001
[8] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. · Zbl 0095.12201
[9] James Pickands III, Maxima of stationary Gaussian processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 190 – 223. · Zbl 0158.16702 · doi:10.1007/BF00532637
[10] David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463 – 501. · doi:10.1002/j.1538-7305.1962.tb02419.x
[11] V. A. Volkonskiĭ and Ju. A. Rozanov, Some limit theorems for random functions. II, Teor. Verojatnost. i Primenen. 6 (1961), 202 – 215 (Russian, with English summary).
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.