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On three basic results in the theory of stationary point processes

Author: M. R. Leadbetter
Journal: Proc. Amer. Math. Soc. 19 (1968), 115-117
MSC: Primary 60.50
MathSciNet review: 0221584
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Abstract: A simple, unified treatment is given for three basic results in the theory of stationary streams of events (point processes). These results are the basic theorem of Khintchine concerning the existence of a stream intensity, Korolyuk's theorem, and a fundamental lemma of Dobrushin giving sufficient conditions for a stationary stream to be orderly in the sense of Khintchine [2].

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

  • [1] Harald Cramér and M. R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1966.
  • [2] A. Y. Khintchine, Mathematical methods in the theory of queueing, Translated by D. M. Andrews and M. H. Quenouille. Griffin’s Statistical Monographs & Courses, No. 7, Hafner Publishing Co., New York, 1960. MR 0115224
  • [3] Klaus Matthes, Stationäre zufällige Punktfolgen. I, Jber. Deutsch. Math.-Verein 66 (1963/1964), no. Abt. 1, 66–79 (German). MR 0160265
  • [4] Czesław Ryll-Nardzewski, Remarks on processes of calls, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 455–465. MR 0140153
  • [5] V. A. Volkonskiĭ, An ergodic theorem for the distribution of sojourn times, Teor. Verojatnost. i Primenen 5 (1960), 357–360 (Russian, with English summary). MR 0149560

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