Boolean, free and monotone cumulants as well relations among them, have proven to be important in the study of non-commutative probability theory. Quite notably, Boolean were successfully used infinite divisibility via Bercovici--Pata bijection. On other hand, recent years concept infinitesimal has been developed, together with notion which can useful context combinatorial questions. In this ...

Two results are presented on a SVD-like decomposition of 4th-order tensors. This is motivated by an array processing problem: consider an array of m sensors listening at n independent narrow band sources; the 4th-order cumulants of the array output form a 4th-order rank-deecient symmetric tensor which has a tetradic structure. Finding a tetradic decomposition of this tensor is equivalent to ide...

In this paper, characterizations of the binomial, negative binomial, geometric, Poisson binomial, Hermite and Poisson distributions are done through their factorial cumulants.

– We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use t...

the problem of discrimination between two stationary ar(p) plus noise processes is consideredwhen the noise process are different in two models. the discrimination rule leads to a quadratic form withcumbersome matrices. an approximate and analytic form is given to distribution of the discriminant. thesimulation study has been used to show the performance of discrimination rule. the cumulants of...

Multichannel, non-Gaussian linear processes are modeled via direct and inverse cumulant-based methods using noisy, multivariate output data . The proposed methods are theoretically insensitive to additive Gaussian noise (perhaps colored, with unknown covariance matrix), and are guaranteed to uniquely identify the system matrix within a post-multiplication by a permutation matrix . Asymptoticall...