The truncated Stieltjes moment problem solved by using kernel density functions

摘要

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.