An information complexity index for probability measures on ℝ with all moments

We prove that, each probability meassure on [Formula: see text], with all moments, is canonically associated with (i) a ∗-Lie algebra; (ii) a complexity index labeled by pairs of natural integers. The measures with complexity index [Formula: see text] consist of two disjoint classes: that of all measures with finite support and the semi-circle-arcsine class (the discussion in Sec. 4.1 motivates this name). The class [Formula: see text] coincides with the [Formula: see text]-measures in the finite support case and includes the semi-circle laws in the infinite support case. In the infinite support case, the class [Formula: see text] includes the arcsine laws, and the class [Formula: see text] appeared in central limit theorems of quantum random walks in the sense of Konno. The classes [Formula: see text], with [Formula: see text], do not seem to be present in the literature. The class [Formula: see text] includes the Gaussian and Poisson measures and the associated ∗-Lie algebra is the Heisenberg algebra. The class [Formula: see text] includes the non-standard (i.e. neither Gaussian nor Poisson) Meixner distributions and the associated ∗-Lie algebra is a central extension of [Formula: see text]. Starting from [Formula: see text], the ∗-Lie algebra associated to the class [Formula: see text] is infinite dimensional and the corresponding classes include the higher powers of the standard Gaussian.

The Jackson Queueing Network Model Built Using Poisson Measures. Application To A Bank Model

In this paper we will build a bank model using Poisson measures and Jackson queueing networks. We take into account the relationship between the Poisson and the exponential distributions, and we consider for each credit/deposit type a node where shocks are modeled as the compound Poisson processes. The transmissions of the shocks are modeled as moving between nodes in Jackson queueing networks, the external shocks are modeled as external arrivals, and the absorption of shocks as departures from the network.

STUDIES IN FRACTIONAL POISSON MEASURES

In this paper we investigate the quasi-invariance property of fractional Poisson measures with respect to the diffeomorphism subgroup and we construct spaces of test and generalized functions associated to the corresponding fractional Lebesgue-Poisson measures.