Iterated Random Functions and Slowly Varying Tails

Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribu...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Dyszewski, Piotr
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Dyszewski, Piotr
description Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when $\Psi_0(t) \approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\log^+(A_0\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\log^+(A_0\vee B_0)$. In particular we will obtain new results for the random difference equation $R_{n+1} = A_{n+1}R_n+B_{n+1}$..
doi_str_mv 10.48550/arxiv.1408.1658
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1408_1658</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1408_1658</sourcerecordid><originalsourceid>FETCH-LOGICAL-a658-4398fdf6fc1135d3a0b28fafbfd1e606f0abb8597db05b8882f4c345d5456cc33</originalsourceid><addsrcrecordid>eNotzrFOwzAUhWEvDFXp3qnyCyTYsa97O6KKQqVKSBB1ja7t3MpSmqAkQPv2pMB0dJZfnxBLrXKLAOqB-kv6yrVVmGsHOBPFfqx7Guso36iN3VnuPtswpq4d5PTle9N9N1d5pP6a2pMsKTXDvbhjaoZ68b9zUe6eyu1Ldnh93m8fDxlN5cyaDXJkx0FrA9GQ8gUyseeoa6ccK_IeYbOOXoFHxIJtMBYiWHAhGDMXq7_sr7n66NN5UlQ3e3Wzmx9x8D6Y</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Iterated Random Functions and Slowly Varying Tails</title><source>arXiv.org</source><creator>Dyszewski, Piotr</creator><creatorcontrib>Dyszewski, Piotr</creatorcontrib><description>Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when $\Psi_0(t) \approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\log^+(A_0\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\log^+(A_0\vee B_0)$. In particular we will obtain new results for the random difference equation $R_{n+1} = A_{n+1}R_n+B_{n+1}$..</description><identifier>DOI: 10.48550/arxiv.1408.1658</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2014-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1408.1658$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1408.1658$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dyszewski, Piotr</creatorcontrib><title>Iterated Random Functions and Slowly Varying Tails</title><description>Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when $\Psi_0(t) \approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\log^+(A_0\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\log^+(A_0\vee B_0)$. In particular we will obtain new results for the random difference equation $R_{n+1} = A_{n+1}R_n+B_{n+1}$..</description><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrFOwzAUhWEvDFXp3qnyCyTYsa97O6KKQqVKSBB1ja7t3MpSmqAkQPv2pMB0dJZfnxBLrXKLAOqB-kv6yrVVmGsHOBPFfqx7Guso36iN3VnuPtswpq4d5PTle9N9N1d5pP6a2pMsKTXDvbhjaoZ68b9zUe6eyu1Ldnh93m8fDxlN5cyaDXJkx0FrA9GQ8gUyseeoa6ccK_IeYbOOXoFHxIJtMBYiWHAhGDMXq7_sr7n66NN5UlQ3e3Wzmx9x8D6Y</recordid><startdate>20140807</startdate><enddate>20140807</enddate><creator>Dyszewski, Piotr</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20140807</creationdate><title>Iterated Random Functions and Slowly Varying Tails</title><author>Dyszewski, Piotr</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a658-4398fdf6fc1135d3a0b28fafbfd1e606f0abb8597db05b8882f4c345d5456cc33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Dyszewski, Piotr</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dyszewski, Piotr</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Iterated Random Functions and Slowly Varying Tails</atitle><date>2014-08-07</date><risdate>2014</risdate><abstract>Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when $\Psi_0(t) \approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\log^+(A_0\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\log^+(A_0\vee B_0)$. In particular we will obtain new results for the random difference equation $R_{n+1} = A_{n+1}R_n+B_{n+1}$..</abstract><doi>10.48550/arxiv.1408.1658</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.1408.1658
ispartof
issn
language eng
recordid cdi_arxiv_primary_1408_1658
source arXiv.org
subjects Mathematics - Probability
title Iterated Random Functions and Slowly Varying Tails
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T21%3A33%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Iterated%20Random%20Functions%20and%20Slowly%20Varying%20Tails&rft.au=Dyszewski,%20Piotr&rft.date=2014-08-07&rft_id=info:doi/10.48550/arxiv.1408.1658&rft_dat=%3Carxiv_GOX%3E1408_1658%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true