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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 51, Issue 2
  • April 1955, pp. 313-319

A use of complex probabilities in the theory of stochastic processes

  • D. R. Cox (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100030231
  • Published online: 24 October 2008
Abstract
ABSTRACT

The exponential distribution is very important in the theory of stochastic processes with discrete states in continuous time. A. K. Erlang suggested a method of extending to other distributions methods that apply in the first instance only to exponential distributions. His idea is generalized to cover all distributions with rational Laplace transforms; this involves the formal use of complex transition probabilities. Properties of the method are considered.

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(6)D. G. Kendall Biometrika, 35 (1948), 316.

(9)E. Lukacs and O. SzÁsz J. Res. nat. Bur. Stand. 48 (1952), 139.

(10)E. Lukacs and O. SzÁsz J. Res. nat. Bur. Stand. 52 (1954), 153.

(11)F. Pollaczek Math. Z. 32 (1930), 64 and 729.

(14)J. L. Walsh Interpolation and approximation by rational functions in the complex domain (Colloq. Publ. Amer. math. Soc., New York, 1935).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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