Local Limit Theorems for Poisson's Binomial in the Case of Infinite Expectation

Italo Simonelli, Lucia D. Simonelli

Let $V_n=X_{1,n}+X_{2,n}+\cdots +X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $λ_{n} = \sum\limits_{i=1…