Consider a sequence of dependent events, where each has uniformly small conditional probability given the past, and the sum of the conditional probabilities is approximately constant at $a$. Then the number of events which occur is approximately Poisson with parameter $a$. An explicit bound is given on the variation distance.
"The Poisson Approximation for Dependent Events." Ann. Probab. 2 (2) 256 - 269, April, 1974. https://doi.org/10.1214/aop/1176996707