Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T13:50:42.735Z Has data issue: false hasContentIssue false
  • English
  • Français

The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables

Published online by Cambridge University Press:  24 October 2008

D. R. Cox
D. R. Cox
Affiliation:
Statistical Laboratory Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Certain stochastic processes with discrete states in continuous time can be converted into Markov processes by the well-known method of including supplementary variables. It is shown that the resulting integro-differential equations simplify considerably when some distributions associated with the process have rational Laplace transforms. The results justify the formal use of complex transition probabilities. Conditions under which it is likely to be possible to obtain a solution for arbitrary distributions are examined, and the results are related briefly to other methods of investigating these processes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 3 , July 1955 , pp. 433 - 441
Copyright
Copyright © Cambridge Philosophical Society 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Brockmeyer, E., Halstrøm, H. L. and Jensen, A.The life and works of A. K. Erlang (Copenhagen, 1948).Google Scholar
(2)Cox, D. R.Proc. Camb. phil. Soc. 51 (1955), 313.CrossRefGoogle Scholar
(3)Kendall, D. G.J.R. statist. Soc. B, 13 (1951), 153.Google Scholar
(4)Kendall, D. G.Ann. math. Statist. 24 (1953), 338.CrossRefGoogle Scholar
(5)Kronig, R.Physica, 's Grav., 10 (1943), 215.CrossRefGoogle Scholar