Nonstandard characterization of convergence in law for $D[0,1]$-valued random variables

Nonstandard Characterization of Convergence in Law for D[0,1]-valued Random Variables

D. Landers and L. Rogge Abstract. We prove for random variables with values in the space D[0; 1] of cadlag functions | endowed with the supremum metric | that convergence in law is equivalent to nonstandard constructions of internal S-cadlag processes, which represent up to an in nitesimal error the limit process. It is not required as earlier, that the limit process is concentrated on the spac...

On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.

Dominated Convergence for Fuzzy Random Variables

Stable Poisson Convergence for Integer-valued Random Variables

Abstract. In this paper, we obtain some stable Poisson Convergence Theorems for arrays of integer-valued dependent random variables. We prove that the limiting distribution is a mixture of Poisson distribution when the conditional second moments on a given σ-algebra of the sequence converge to some positive random variable. Moreover, we apply the main results to the indicator functions of rowis...

On the Complete Convergence ofWeighted Sums for Dependent Random Variables

We study the limiting behavior of weighted sums for negatively associated (NA) random variables. We extend results in Wu (1999) and a theorem in Chow and Lai (1973) for NA random variables.