Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study
Journal of Approximation Theory
Entropy-convergence in Stieltjes and Hamburger moment problem
Applied Mathematics and Computation
SIAM Journal on Optimization
On the Relation Between Option and Stock Prices: A Convex Optimization Approach
Operations Research
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
On powers of Stieltjes moment sequences, II
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Journal of Computational and Applied Mathematics
Asymptotic Probability Extraction for Nonnormal Performance Distributions
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In this work the problem of the approximate numerical determination of a semi-infinite supported, continuous probability density function (pdf) from a finite number of its moments is addressed. The target space is carefully defined and an approximation theorem is proved, establishing that the set of all convex superpositions of appropriate Kernel Density Functions (KDFs) is dense in this space. A solution algorithm is provided, based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics. The solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution. A parsimonious formulation of the proposed solution procedure, based on a novel sequentially adaptive scheme is developed, enabling a very efficient moment data inversion. The whole methodology is fully illustrated by numerical examples.