Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1968-0221584-4
MathSciNet review: 0221584
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] Y. A. Khintchine, Mathematical methods in the theory of queueing, Griffin, London, 1960. MR 0115224 (22:6026)
  • [3] K. Matthes, Stationäre Zufällige Punktfolgen. I, Jber. Deutsch. Math.-Verein. 66 (1963), 66-79. MR 0160265 (28:3479)
  • [4] C. Ryll Nardzewski, Remarks on processes of calls, Proc. Fourth Berkeley Sympos. Math. Stat. & Prob., Vol. 2, 1961, pp. 455-466. MR 0140153 (25:3575)
  • [5] V. A. Volkonski, An ergodic theorem on the distribution of the duration of fades, Teor. Verojatnost. i Primenen. 5 (1960), 360-361. MR 0149560 (26:7045)

Similar Articles

Retrieve articles in Proceedings 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/S0002-9939-1968-0221584-4
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society