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A recursion theorem on solving differential-difference equations and applications to some stochastic processes

Published online by Cambridge University Press:  14 July 2016

Norman C. Severo
Norman C. Severo*
Affiliation:
State University of New York, Buffalo
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Summary

A recursive procedure leading to the solution of triangular systems of differential-difference equations is presented. It is shown that the equations for special families of multi-dimensional pure birth processes and pure death processes can be represented as such a system. The theory is used to resolve a difficult problem of stochastic cross-infection among groups. Additional applications to problems in epidemic theory are discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 673 - 681
Copyright
Copyright © Applied Probability Trust 

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