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Approximation of probabilistic Laplace transforms and their inverses. (English) Zbl 1259.65206

Summary: 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.

MSC:

65R10 Numerical methods for integral transforms
44A10 Laplace transform
65R32 Numerical methods for inverse problems for integral equations
65C50 Other computational problems in probability (MSC2010)
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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