On the time of first level crossing and inverse Gaussian distribution

2017/08/29 by Malinovskii, Vsevolod K.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.08665

Abstract

We propose a new approximation for the distribution of the time of the first level u crossing by the random process \homVs-cs, where \homVs, s>0, is compound renewal process and c>0. It is competitive with respect to existing approximations, particularly in the region around the critical point c=\cS which separates processes with positive and negative drifts. This approximation is tightly related to inverse Gaussian distributions.

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