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

Manfred Heinz Denker, Xiaofei Zheng

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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.

Original languageEnglish (US)
Pages (from-to)2448-2462
Number of pages15
JournalStochastic Processes and their Applications
Volume128
Issue number7
DOIs
Publication statusPublished - Jul 1 2018

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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