We find a one parameter family of quadratic Poisson structures on R 4 × SL(2, C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz group, as well as b) that it reduces to the standard Poincaré algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer t...

We apply the Stein-Chen method for Poisson approximation to spin-half Isingtype models, in positive external eld, which satisfy the FKG inequality. In particular we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is ...

We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal stopping of the limiting Poisson process. The optimal stopping of the involved Poisson processes is reduced...

This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in Rn (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of volume preserving diffeomorphism group. This is interesting and nontrivial because in Eulerian representation, the time t maps need not be C from th...

We prove that the periodic initial value problem for a modified Euler-Poisson equation is well-posed for initial data in Hs(Tm) when s > m/2 + 1. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem. After presenting a formal derivation of the equation on the semidirect product space Diff C∞(T) as a Hamiltonian equation, we concentrate on one space di...

This paper develops a censored generalized Poisson regression model that can be used to predict a response variable that is a2ected by one or more explanatory variables. The censored generalized Poisson regression model is suitable for modeling count data that exhibit either overor under-dispersion. The regression parameters are estimated by the method of maximum likelihood and approximate test...

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically dis...

Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density λ c for d-dimensional Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λ c ≈ 1.44, while the best theoretical bounds obtained thus far...

Abstract– Uniformization is a powerful numerical technique for the analysis of continuous time Markov chains that possesses a probabilistic interpretation. In this paper, we propose the combination of the embedded Markov chain approach for queues with uniformization to analyze GI/M/s/c queues. The main steps of the procedure are: (1) To compute the mixed-Poisson probabilities associated to the ...