Vol. 7, No. 2, 2012

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Approximation of probabilistic Laplace transforms and their inverses

Guillaume Coqueret

Vol. 7 (2012), No. 2, 231–246
Abstract

We present a method to approximate the law of positive random variables defined by their Laplace transforms. It is based on the study of the error in the Laplace domain and allows for many behaviors of the law, both at 0 and infinity. In most cases, both the Kantorovich/Wasserstein error and the Kolmogorov–Smirnov error can be accurately computed. Two detailed examples illustrate our results.

Keywords
approximation, Laplace transform inversion, completely monotone functions, Kantorovich distance
Mathematical Subject Classification 2010
Primary: 65R32
Secondary: 65C50
Milestones
Received: 23 March 2012
Revised: 27 July 2012
Accepted: 16 August 2012
Published: 8 January 2013
Authors
Guillaume Coqueret
ESSEC Business School / Université de Lille-1
Avenue Bernard Hirsch
95000 Cergy-Pontoise
France