Computing Inverses of Stieltjes Transforms of Probability Measures

James Chen; Sheehan Olver

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arxiv 2410.16178 v1 pith:WZ5NC2QV submitted 2024-10-21 math.NA cs.NA

Computing Inverses of Stieltjes Transforms of Probability Measures

James Chen , Sheehan Olver This is my paper

classification math.NA cs.NA

keywords inversesprobabilitystieltjescomputemeasurestransformalgorithmsapplications

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The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential to compute the inverses of the Stieltjes transform, which might be multivalued. This paper establishes conditions bounding the number of inverses based on properties of the measure which can be combined with contour integral-based root finding algorithms to rigorously compute all inverses.

Computing Inverses of Stieltjes Transforms of Probability Measures

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