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

Manfred Heinz Denker, Xiaofei Zheng

Research output: Contribution to journalArticle

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
StatePublished - Jul 1 2018

Fingerprint

Conditional Limit Theorems
Local Limit Theorem
Local Time
Stationary Process
Topology
Weak Topology
Imply
Integer

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Denker, Manfred Heinz ; Zheng, Xiaofei. / On the local times of stationary processes with conditional local limit theorems. In: Stochastic Processes and their Applications. 2018 ; Vol. 128, No. 7. pp. 2448-2462.
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On the local times of stationary processes with conditional local limit theorems. / Denker, Manfred Heinz; Zheng, Xiaofei.

In: Stochastic Processes and their Applications, Vol. 128, No. 7, 01.07.2018, p. 2448-2462.

Research output: Contribution to journalArticle

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