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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Integral representations for Markov transition probabilities
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by David G. Kendall PDF
Bull. Amer. Math. Soc. 64 (1958), 358-362
References
  • Mark Kac, Random walk and the theory of Brownian motion, Amer. Math. Monthly 54 (1947), 369–391. MR 21262, DOI 10.2307/2304386
  • Samuel Karlin and James McGregor, Representation of a class of stochastic processes, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 387–391. MR 71665, DOI 10.1073/pnas.41.6.387
  • David G. Kendall, Unitary dilations of Markov transition operators, and the corresponding integral representations for transition-probability matrices, Probability and statistics: The Harald Cramér volume (edited by Ulf Grenander), Almqvist & Wiksell, Stockholm; John Wiley & Sons, New York, N.Y., 1959, pp. 139–161. MR 0116389
  • David G. Kendall, Unitary dilations of one-parameter semigroups of Markov transition operators, and the corresponding integral representations for Markov processes with a countable infinity of states, Proc. London Math. Soc. (3) 9 (1959), 417–431. MR 116390, DOI 10.1112/plms/s3-9.3.417
    • 5. D. G. Kendall, Geometric ergodicity in the theory of queues, to appear.
  • A. Kolmogoroff, Zur Theorie der Markoffschen Ketten, Math. Ann. 112 (1936), no. 1, 155–160 (German). MR 1513044, DOI 10.1007/BF01565412
  • W. Ledermann and G. E. H. Reuter, Spectral theory for the differential equations of simple birth and death processes, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 321–369. MR 60103, DOI 10.1098/rsta.1954.0001
  • Edgar Reich, Waiting times when queues are in tandem, Ann. Math. Statist. 28 (1957), 768–773. MR 93060, DOI 10.1214/aoms/1177706889
    • 9. B. Sz.-Nagy, Prolongements des transformations de l’espace de Hilbert qui sortent de cet espace, Appendix, 1955, to F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionnelle, Budapest, 1952.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 64 (1958), 358-362
  • DOI: https://doi.org/10.1090/S0002-9904-1958-10230-X
  • MathSciNet review: 0126880