Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

D. R. Coxa1

a1 Statistical Laboratory Cambridge

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.

(Received November 09 1954)