Hamburger moment problem for powers and products of random variables

2014 ◽  
Vol 154 ◽  
pp. 166-177 ◽  
Author(s):  
Jordan Stoyanov ◽  
Gwo Dong Lin ◽  
Anirban DasGupta
Keyword(s):  
Moment Problem ◽  
Random Variables ◽  
Hamburger Moment Problem ◽  
Products Of Random Variables

On the moment determinacy of the distributions of compound geometric sums

2002 ◽  
Vol 39 (3) ◽  
pp. 545-554 ◽  
Author(s):  
Gwo Dong Lin ◽  
Jordan Stoyanov
Keyword(s):  
Real Line ◽  
Moment Problem ◽  
Random Variables ◽  
Hamburger Moment Problem ◽  
Stieltjes Moment Problem ◽  
The Moment ◽  
Geometric Sums

We deal with compound geometric sums of independent positive random variables and study the moment problem for the distributions of such sums (the Stieltjes moment problem). We find conditions under which the distributions are uniquely determined by their moments. We also treat related topics, including the Hamburger moment problem involving random variables on the whole real line. Some conjectures are outlined.

On the moment determinacy of the distributions of compound geometric sums

2002 ◽  
Vol 39 (03) ◽  
pp. 545-554 ◽  
Author(s):  
Gwo Dong Lin ◽  
Jordan Stoyanov
Keyword(s):  
Real Line ◽  
Moment Problem ◽  
Random Variables ◽  
Hamburger Moment Problem ◽  
Stieltjes Moment Problem ◽  
The Moment ◽  
Geometric Sums

We deal with compound geometric sums of independent positive random variables and study the moment problem for the distributions of such sums (the Stieltjes moment problem). We find conditions under which the distributions are uniquely determined by their moments. We also treat related topics, including the Hamburger moment problem involving random variables on the whole real line. Some conjectures are outlined.

scholarly journals An extended Hamburger moment problem

1985 ◽  
Vol 28 (2) ◽  
pp. 167-183 ◽  
Author(s):  
Olav Njåstad
Keyword(s):  
Distribution Function ◽  
Moment Problem ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Moment Problems ◽  
Real Numbers ◽  
Orthogonal Functions ◽  
Hamburger Moment Problem ◽  
Hankel Determinants ◽  
Necessary And Sufficient

The classical Hamburger moment problem can be formulated as follows: Given a sequence {cn:n=0,1,2,…} of real numbers, find necessary and sufficient conditions for the existence of a distribution function ψ (i.e. a bounded, real-valued, non-decreasing function) on (– ∞,∞) with infinitely many points of increase, such that , n = 0,1,2, … This problem was posed and solved by Hamburger [5] in 1921. The corresponding problem for functions ψ on the interval [0,∞) had already been treated by Stieltjes [15] in 1894. The characterizations were in terms of positivity of Hankel determinants associated with the sequence {cn}, and the original proofs rested on the theory of continued fractions. Much work has since been done on questions connected with these problems, using orthogonal functions and extension of positive definite functionals associated with the sequence. Accounts of the classical moment problems with later developments can be found in [1,4,14]. Good modern accounts of the theory of orthogonal polynomials can be found in [2,3].

scholarly journals Chebyshev Inequalities for Products of Random Variables

2018 ◽  
Vol 43 (3) ◽  
pp. 887-918 ◽  
Author(s):  
Napat Rujeerapaiboon ◽  
Daniel Kuhn ◽  
Wolfram Wiesemann
Keyword(s):  
Random Variables ◽  
Products Of Random Variables ◽  
Chebyshev Inequalities

Analytic functions associated with strong Hamburger moment problems

2009 ◽  
Vol 52 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Olav Njåstad
Keyword(s):  
Moment Problem ◽  
Analytic Functions ◽  
Moment Problems ◽  
Hamburger Moment Problem ◽  
Growth Properties

AbstractWe complete the investigation of growth properties of analytic functions connected with the Nevanlinna parametrization of the solutions of an indeterminate strong Hamburger moment problem.

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