A generalized local limit theorem for mixing semi-flows

Abstract

Let $S_t:M \to M$ be a semi-flow preserving a probability measure $\mu$ on a compact manifold $M$ and $g:M\to\mathbb{R}$ a real-valued Borel measurable function. We show a generalized local limit theorem for the stationary process $\{g\circ S_t;t\geq 0\}$ on the probability space $(M,\mu)$ under certain conditions.