Skip to main content
×
Home
    • Aa
    • Aa

A use of complex probabilities in the theory of stochastic processes

  • D. R. Cox (a1)
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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(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).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 93 *
Loading metrics...

Abstract views

Total abstract views: 398 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd May 2017. This data will be updated every 24 hours.