Sentence examples for moment problem for from inspiring English sources

Stoyanov et al. (2014) and Lin and Stoyanov (2015) investigated the moment problem for products of i.i.d.i.d

Lin and Stoyanov (2002) and Gut (2003) studied the moment problem for random sums of independently identically distributed (i.i.d).i.d

Finally, we review the most recent moment problem for products of independent random variables with different distributions, which occur naturally in stochastic modelling of complex random phenomena.

Finally, in Section 6 we review the most recent results about the moment problem for products of independent random variables with different distributions.

In this paper we solve the truncated moment problem for cubic column relations in M 3) of the form Z3= itZ+uZ¯ (u,t∈R); we do this by checking consistency.

Instead, we note that if α∈ 0,2], the mgf of |X|α exists by its density function above, and hence |X|2α is M-det by Hardy's criterion. There are some ramifications of the moment problem for normal random variables.

In [9], the authors transfer high dimensional Cauchy problem for Laplace equation into moment problem, and then construct a series of polynomial functions to approximate solutions of the moment problem.

Besides this, the algebraic moment problem by Mammana [2] asks for the existence and construction of a finite atomic random variable with a given finite moment structure.

For the truncated moment problem associated to a complex sequence γ(2n)="{γij}i,j∈Z+,i+j⩽2n to have a representing measure μ, it is necessary for the moment matrix M n) to be positive semidefinite, and for the algebraic variety Vγ to satisfy rankM n)⩽cardVγ as well as a consistency condition: the Riesz functional vanishes on every polynomial of degree at most 2n that vanishes on Vγ.

The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m>5 10) due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities.

However, these conditions are not sufficient for non-extremal sextic or higher-order truncated moment problems.