Any Random Variable with Finite Moments Is a Sum of Two Variables with Determinate Moment Problem
Константин Владимирович Лыков · Theory of Probability and Its Applications · 2018
It is known that two random variables may have equal moments of all orders but unequal distributions. If, for a given random variable, there does not exist a differently distributed random variable with the same moments, then the original random variable is said to have determinate moment problem, or one says that the moment problem has a unique solution. It is shown that any random variable such that all its moments are finite can be represented as a sum of two disjoint variables, and each of them has determinate moment problem.