This paper shows how to calculate solutions to Poisson's equation for the waiting time sequence of the recurrent M/G/1 queue. The solutions are used to construct martingales that permit us to study additive functionals associated with the waiting time sequence. These martingales provide asymptotic expressions, for the mean of additive functionals, that reeect dependence on the initial state of ...

We give a new proof of a formula of Bloch for a special value of a certain Eisenstein series of weight one with an additive character.

This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by...

A seasonal additive nonlinear vector autoregression (SANVAR) model is proposed for multivariate seasonal time series to explore the possible interaction among the various univariate series. Significant lagged variables are selected and additive autoregression functions estimated based on the selected variables using spline smoothing method. Conservative confidence bands are constructed for the ...

There is a simple type of electric network termed a series-parallel connection which occurs frequently in both theoretical and applied electrical engineering. One reason for the importance of series-parallel connection stems from the fact that the joint resistance is easily evaluated by the following two rules due to Ohm: 0 s. Resistance is additive for resistors in series. 0 P. Reciprocal resi...

We consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements ...

In spatial epidemiology, when applying Generalized Additive Models (GAMs) with a bivariate locally weighted regression smooth over longitude and latitude, a natural hypothesis is whether location is associated with an outcome. An approximate chi-square test (ACST) is available but has an inflated type I error rate. Permutation tests provide alternatives. This research evaluated powers of ACST a...