In Siotani & Fujikoshi (1984), a precise local limit theorem for the multinomial distribution is derived by inverting Fourier transform, where error terms are explicit up to order $N^{-1}$. this paper, we give an alternative (conceptually simpler) proof based on Stirling's formula and careful handling of Taylor expansions, show how result can be used approximate probabilities most subsets $\mat...

In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables: lim n→∞ (1/ log n)∑n k=1 (I(a k ≤ S k < b k )/k)P(a k ≤ S k < b k ) = 1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central...

SUMMARY A functional central limit theorem for a local square integrable martingale with persistent disconti-nuities is given. By persistent discontinuities, it is meant that the martingale has jumps which do not vanish asymptotically. This central limit theorem is motivated by problems in the analysis of longitudinal and life history data.

A discrete time multitype (p-type) branching random walk on the real line R&nbsp;is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

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...

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviations principl...