SADDLEPOINT APPROXIMATIONS FOR STOCHASTIC-PROCESSES WITH TRUNCATED CUMULANT GENERATING-FUNCTIONS

Only in the simplest scenarios of population dynamics can the Kolmogor ov forward differential equation for the cumulant generating function be solved explicitly. A device which is currently gaining in popularit y is the differentiation of this equation up to order j, thereby obtai ning a set of j equations for the cumulants {kappa(i)}, and then solvi ng these equations by placing kappa(i) = 0 for all i > j. Here we show how the saddlepoint approximation may be used to investigate the effe ct that this technique has on the underlying probability structure thr ough application to the logistic and power-law logistic processes.