Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4628898 | Applied Mathematics and Computation | 2013 | 5 Pages |
Abstract
In this note we consider Laplace transforms of probability distribution functions F(t)F(t) on (0,∞)(0,∞) that have finite integer moments of all orders. We construct a family Fω(t)Fω(t) of distribution functions, whose Laplace transforms differ from that of F(t)F(t) by as little as we want, but such that Fω(t)Fω(t) has a discrete part whereas F(t)F(t) has a density f(t)f(t). Thus we provide one more example of why Laplace transform inversion on the real line is a difficult, ill-conditioned, inverse problem.
Keywords
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
H. Gzyl, A. Tagliani, M. Milev,