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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics