Let k:n = Xk,n − Xk−1,n(k = 1, 2, . . . , n+1) be the spacings based on uniform order statistics, provided X0,n = 0 and Xn+1,n = 1. Obtained from uniform spacings, ordered uniform spacings 0 = 0,n < 1,n < · · · < n+1,n , are discussed in the present paper. Distributional and limit results for them are in the focus of our attention.

For n particles diiusing throughout R (or R d), let n;t (A), A 2 B, t 0, be the random measure that counts the number of particles in A at time t. It is shown that for some basic models (Brownian particles with or without branching and diiusion with a simple interaction) the processes f(n;t () ? E n;t ())= p n : t 2 0; M]; 2 C L (R)g, n 2 N, converge in law uniformly in (t;). Previous results c...

In literature of Fourier transforms and Wavelet transforms, the basic space is L2(R). From the point of view of signal analysis, a signal f ∈ L2(R) can only be transient (or “wavelets”). During recent years in some application areas, it has become more common to motivate a theory via persistent rather than transient signals (e.g., [16, 28, 30, 42]). To work on persistent signals, people have to...

Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let f : X → X where X is a compact metric space and f is continuous, onto and piecewise one-to-one and Y := lim ←− (X, f). Then starting with a measure μ1 on the Borel sets B(X), we recursively construct a sequence of probability measures {μn}n=1 on B(X) satisfying ...

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...