Bell Numbers in Matsunaga's and Arima's Genjikō Combinatorics: Modern Perspectives and Local Limit Theorems

On Local and Ratio Limit Theorems

Local Limit Theorems for Free

Almost sure local limit theorems

Chung and Erdös (1951) are among the first to prove some form of an almost sure local limit theorem (cf. Csáki et al., 1993). Here we propose a formulation of such statements and discuss related problems. Surely, Frits will enjoy them. c ©2001, June 19.

Central and Local Limit Theorems in Markov Dependent Random Variables

We consider an irreducible and aperiodic Markov chain {kn}n=0 over the finite state space E = {1, . . . , p} with positive regular transition matrix P = {pij} and additive component {Un} such that {Sn} = {(kn, Un)} is also a Markov chain over the state space E1 = E × R. We prove a central and a local limit theorem for this chain when the probability density functions of {Sn}, conditional on the...

Central and Local Limit Theories in Markov Dependent Random Variables