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

Manfred Denker and Xiaofei Zheng

Stochastic Processes and their Applications, 2018, vol. 128, issue 7, 2448-2462

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.

Date: 2018
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DOI: 10.1016/j.spa.2017.09.012

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