Consider {Xj, j [greater-or-equal, slanted] 1}, a sequence of i.i.d., positive, integer-valued random variables. Let Kn denote the number of the integer j [set membership, variant] {1,2,...,n} for which Xj = max1[less-than-or-equals, slant]m[less-than-or-equals, slant]n Xm. In this paper we...

In this paper we study limit theorems for a class of correlated Bernoulli processes. We obtain the strong law of large numbers, central limit theorem and the law of the iterated logarithm for the partial sums of the Bernoulli random variables.

In this paper we study the asymptotic joint behavior of the maximum and the partial sum of a multivariate Gaussian sequence. The multivariate maximum is defined to be the coordinatewise maximum. Results extend univariate results of McCormick and Qi. We show that, under regularity conditions, if...

Consider a Galton-Watson process with immigration. The limiting distributions of the nonsequential estimators of the offspring mean have been proved to be drastically different for the critical case and subcritical and supercritical cases. A sequential estimator, proposed by Sriram et al. (Ann....

This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the...