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Mathematical Medicine and Biology 1998 15(1):41-52; doi:10.1093/imammb/15.1.41
© 1998 by Institute of Mathematics and its Applications
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Saddlepoint approximations for stochastic processes with truncated cumulant generating functions

ERIC RENSHAW

Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde 26 Richmond Street, Glasgow G1 1XH, UK

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 {equiv} 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


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