Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Upcrossing probabilities for stationary Gaussian processes


Author: James Pickands
Journal: Trans. Amer. Math. Soc. 145 (1969), 51-73
MSC: Primary 60.50
DOI: https://doi.org/10.1090/S0002-9947-1969-0250367-X
MathSciNet review: 0250367
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] T. W. Anderson, An introduction to multivariate statistical analysis, Wiley, New York, 1958. MR 0091588 (19:992a)
  • [2] Yu. K. Belyaev, Continuity and Hölder's conditions for sample functions of stationary Gaussian processes, Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, 1961, pp. 23-33. MR 0143256 (26:815)
  • [3] S. M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35 (1964), 502-516. MR 0161365 (28:4572)
  • [4] H. Cramér, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J., 1951.
  • [5] -, On the intersections between the trajectories of a normal stationary stochastic process and a high level, Ark. Mat. 6 (1966), 337-349. MR 0203820 (34:3667)
  • [6] H. Cramér and M. R. Leadbetter, Stationary and related stochastic processes; sample function properties and their applications, Wiley, New York, 1955.
  • [7] A. N. Kolmogorov and B. V. Gnedenko, Limit distributions for sums of independent random variables, Addison-Wesley, Reading, Mass., 1954. MR 0062975 (16:52d)
  • [8] M. Loeve, Probability theory, Van Nostrand, Princeton, N. J., 1963. MR 0203748 (34:3596)
  • [9] J. Pickands, Maxima of stationary Gaussian processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 190-223. MR 0217866 (36:955)
  • [10] D. Slepian, The one sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463-501. MR 0133183 (24:A3017)
  • [11] V. A. Volkonski and Yu. A. Rozanov, Some limit theorems for random functions. II, Teor. Verojatnost. i Primenen. 6 (1961), 202-215 = Theor. Probability Appl. 6 (1961), 186-198. MR 0137141 (25:597)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.50

Retrieve articles in all journals with MSC: 60.50


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0250367-X
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society