Let $(X_n)_{n\in\mathbb N}$ be a time-homogeneous Markov chain with stationary distribution $\mu$. Assume $\mu$ has a density with respect to some reference measure $p$ and let $f$ be an $\mu$-integrable function. Consider the estimator $$A_n:=\frac1n\sum_{i=1}^n\frac fp(X_i)\;\;\;\text{for }n\in\mathbb N$$ of $$\int f\:{\rm d}\lambda.$$
In a paper I've read that "stratification implies that a sample should preferably have a private volume of size $\frac1{np}$". What is actually meant by that and how is this volume derived?