Journal Article

Saddlepoint approximations for stochastic processes with truncated cumulant generating functions

ERIC RENSHAW

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 15, issue 1, pages 41-52
Published in print March 1998 | ISSN: 1477-8599
Published online March 1998 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/15.1.41
Saddlepoint approximations for stochastic processes with truncated cumulant generating functions

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Only in the simplest scenarios of population dynamics can the Kolmogorov forward differential equation for the cumulant generating function be solved explicitly. A device which is currently gaining in popularity is the differentiation of this equation up to order j, thereby obtaining a set of j equations for the cumulants {ki}, and then solving these equations by placing Ki ≡ 0 for all i > j. Here we show how the saddlepoint approximation may be used to investigate the effect that this technique has on the underlying probability structure through application to the logistic and power-law logistic processes.

Keywords: cumulants; saddlepoint approximation; power-law processes; tail probabilities; truncation; logistic

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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