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

Manfred Heinz Denker; Xiaofei Zheng

doi:10.1016/j.spa.2017.09.012

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

Manfred Heinz Denker, Xiaofei Zheng

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	2448-2462
Number of pages	15
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2017.09.012
State	Published - Jul 1 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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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.",

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