On three basic results in the theory of stationary point processes
HTML articles powered by AMS MathViewer
- by M. R. Leadbetter PDF
- Proc. Amer. Math. Soc. 19 (1968), 115-117 Request permission
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
-
Harald Cramér and M. R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1966.
- A. Y. Khintchine, Mathematical methods in the theory of queueing, Griffin’s Statistical Monographs & Courses, No. 7, Hafner Publishing Co., New York, 1960. Translated by D. M. Andrews and M. H. Quenouille. MR 0115224
- Klaus Matthes, Stationäre zufällige Punktfolgen. I, Jber. Deutsch. Math.-Verein. 66 (1963/64), no. Abt. 1, 66–79 (German). MR 160265
- 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
- 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
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 19 (1968), 115-117
- MSC: Primary 60.50
- DOI: https://doi.org/10.1090/S0002-9939-1968-0221584-4
- MathSciNet review: 0221584