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A use of complex probabilities in the theory of stochastic processes

Published online by Cambridge University Press:  24 October 2008

D. R. Cox
D. R. Cox
Affiliation:
Statistical Laboratory Cambridge
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 2 , April 1955 , pp. 313 - 319
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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