A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory

Marc Kesseboehmer; Sabrina Kombrink

doi:10.3934/dcdss.2017016

A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory

Marc Kesseboehmer, Sabrina Kombrink

Mathematics

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

1 Citation (Scopus)

Abstract

We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

Original language	English
Pages (from-to)	335-352
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	10
Issue number	2
DOIs	https://doi.org/10.3934/dcdss.2017016
Publication status	Published - 30 Apr 2017

Keywords

Ruelle-Perron-Frobenius operator
renewal theory

Access to Document

10.3934/dcdss.2017016Licence: None: All rights reserved

http://www.aimsciences.org/article/doi/10.3934/dcdss.2017016Licence: None: All rights reserved

Cite this

@article{3273bef1eb0f480ea175d90d163b7be0,

title = "A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory",

abstract = "We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.",

keywords = "Ruelle-Perron-Frobenius operator, renewal theory",

author = "Marc Kesseboehmer and Sabrina Kombrink",

year = "2017",

month = apr,

day = "30",

doi = "10.3934/dcdss.2017016",

language = "English",

volume = "10",

pages = "335--352",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory

AU - Kesseboehmer, Marc

AU - Kombrink, Sabrina

PY - 2017/4/30

Y1 - 2017/4/30

N2 - We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

AB - We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

KW - Ruelle-Perron-Frobenius operator

KW - renewal theory

U2 - 10.3934/dcdss.2017016

DO - 10.3934/dcdss.2017016

M3 - Article

SN - 1937-1632

VL - 10

SP - 335

EP - 352

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 2

ER -

A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory

Abstract

Keywords

Access to Document

Fingerprint

Cite this