Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems

TL;DR

This paper addresses finite Markov moment problems with positive and negative branches, establishing criteria for solutions, characterizing non-unique families, and providing a constructive numerical algorithm with proven correctness.

Contribution

It introduces new existence and uniqueness criteria, characterizes non-unique solutions, and develops a constructive algorithm for solving these moment problems.

Findings

Criteria for existence and uniqueness established

Characterization of non-unique solution families

Constructive algorithm proven to compute correct solutions

Abstract

We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families. Moreover, we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution.