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

Access to Document

10.1016/j.spa.2017.09.012

Cite this

@article{f9a33fcebae2427681eb004a561edb32,

title = "On the local times of stationary processes with conditional local limit theorems",

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.",

author = "Denker, {Manfred Heinz} and Xiaofei Zheng",

year = "2018",

month = jul,

day = "1",

doi = "10.1016/j.spa.2017.09.012",

language = "English (US)",

volume = "128",

pages = "2448--2462",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "7",

}

TY - JOUR

T1 - On the local times of stationary processes with conditional local limit theorems

AU - Denker, Manfred Heinz

AU - Zheng, Xiaofei

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85030858462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030858462&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2017.09.012

DO - 10.1016/j.spa.2017.09.012

M3 - Article

AN - SCOPUS:85030858462

VL - 128

SP - 2448

EP - 2462

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 7

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this