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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Upcrossing probabilities for stationary Gaussian processes
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by James Pickands PDF
Trans. Amer. Math. Soc. 145 (1969), 51-73 Request permission
References
  • T. W. Anderson, An introduction to multivariate statistical analysis, Wiley Publications in Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0091588
  • 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. MR 0143256
  • Simeon M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35 (1964), 502–516. MR 161365, DOI 10.1214/aoms/1177703551
  • H. Cramér, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J., 1951.
  • 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). MR 203820, DOI 10.1007/BF02590962
  • H. Cramér and M. R. Leadbetter, Stationary and related stochastic processes; sample function properties and their applications, Wiley, New York, 1955.
  • B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR 0062975
  • Michel Loève, Probability theory, 3rd ed., D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. MR 0203748
  • James Pickands III, Maxima of stationary Gaussian processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 190–223. MR 217866, DOI 10.1007/BF00532637
  • David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463–501. MR 133183, DOI 10.1002/j.1538-7305.1962.tb02419.x
  • 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). MR 0137141
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Additional Information
  • © Copyright 1969 American Mathematical Society
  • 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