This paper investigates the uniform convergence for the Nadaraya-Watson estimators in a non-linear cointegrating regression. Our results provide a optimal convergence rate without the compact set restriction, allowing for martingale innovation structure and the situation that the data regressor sequence is a partial sum of general linear process including fractionally integrated time series. We...

Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the non-uniform point, as well as between the standard point and the nonstandard point, is showed. A new kind of equations, which differ essentially from those in ex...

Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the non-uniform point, as well as between the standard point and the nonstandard point, is showed. A new kind of equations, which differ essentially from those in ex...

Abstract We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.