# On the local times of stationary processes with conditional local limit theorems

## TL;DR

This paper explores how conditional local limit theorems influence the behavior of local times in stationary processes, demonstrating convergence to Mittag-Leffler distributions.

## Contribution

It establishes a link between conditional local limit theorems and the convergence of local times to Mittag-Leffler distributions in stationary processes.

## Key findings

- Conditional local limit theorem implies local time convergence.
- Local times converge to Mittag-Leffler distributions.
- Results hold in weak topology and almost surely.

## Abstract

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions.