On Chung-Teicher type strong law for arrays of vector-valued random variables.
On Chung-Teicher type strong law of large numbers for -mixing random variables.
On complete convergence for -mixingales.
On complete convergence for randomly indexed sums for a case without identical distributions.
On complete convergence in a Banach space.
On complete convergence of the sum of a random number of stable type random elements.
On complete moment convergence for weighted sums of AANA random variables
In this work, a complete moment convergence theorem is obtained for weighted sums of asymptotically almost negatively associated (AANA) random variables without assumption of identical distribution under some mild moment conditions. As an application, the complete convergence theorems for weighted sums of negatively associated (NA) and AANA random variables are obtained. The result not only generalizes the corresponding ones of Sung [13] and Huang et al. [8], but also improves them.
On complete moment convergence for weighted sums of negatively superadditive dependent random variables
In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of...
On conditions for SLLN for martingales with identically distributed increments.
On conditions for the strong law of large numbers in general Banach spaces.
On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
On convergence for sequences of pairwise negatively quadrant dependent random variables
In this paper, some new results on complete convergence and complete moment convergence for sequences of pairwise negatively quadrant dependent random variables are presented. These results improve the corresponding theorems of S. X. Gan, P. Y. Chen (2008) and H. Y. Liang, C. Su (1999).
On entropies for random partitions of the unit segment
We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.
On Feller's criterion for the law of the iterated logarithm.
On limit properties of the reward from a Markov replacement process
On mean values of subadditive processes
On Measures of Uniformly Distributed Sequences and Benford's Law.
On Multivalued Amarts
In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym...
On random split of the segment
We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These...
On recurrence property of Riesz-Raikov sums.