The paper gives estimates of the rate of convergence in the Central Limit Theorems for stochastically continuous cadlag processes proved recently by B ezandry and Fernique (Ann.

Anisotropic singular perturbations of linear hyperbolic problems are considered. A description of the asymptotic behaviour of the solution as ε → 0 is given. In the case of cylindrical domains, we improve the rate of convergence in regions far from the lateral boundary.

We examine the structure of the core of a trading economy with three competitive equilibria as the number of traders (N) is varied. The core first splits into two pieces at N = 5 and then splits a second time into three pieces at N = 12. Both of these splits occur not at a point but as a contiguous gap. We find that the speed of convergence of the core toward the three competitive equilibria is...

Article history: Received 11 September 2016 Received in revised form 4 December 2016 Accepted 6 January 2017 Available online 10 January 2017

This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite dimensional case, our asymptotic result shows the smoothness of the unknown mean function has an effect on the rate of convergence. Our simulaton studies demonstrate...

We consider the normalized sum of n independent identically distributed random variables Xi; i = 1; : : : ; n with the common probability distribution function F (x) and probability density q(y) = F (y). We suppose that the distribution function Fn(y) of the normalized sum converges as n ! 1 to a stable distribution or stable law. The only stable distributions are the normal distributions and t...

We present an original ant model to solve the foraging problem. We describe simulations and provide a convergence analysis. We prove the convergence of the model in the discrete and in the continuous cases. We show that the ant population computes the solution of an optimal control problem and converges in a well defined sense. We discuss the rate of convergence with respect to the number of an...