Beyond Poisson Approximation: Sums of Markovian Bernoulli Variables with Applications to Brownian Motions and Branching Processes

Hua-Ming Wang, Shuxiong Zhang

Let $\{{\eta }_i{\}}_{i\ge 1}$ be a sequence of dependent Bernoulli random variables. While the Poisson approximation for the distribution of ${\sum }_{i=1}^n{\eta }_i$ has been extensively studied…