Multitype branching processes with inhomogeneous Poisson immigration

In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and uncondi...

Full description

Saved in:
Bibliographic Details
Published in:Advances in applied probability 2018-12, Vol.50 (A), p.211-228
Main Authors: Mitov, Kosto V., Yanev, Nikolay M., Hyrien, Ollivier
Format: Article
Language:English
Subjects:
Asymptotic properties
Branching (mathematics)
Fractals
Immigration
Markov processes
Original Article
Poisson distribution
Probability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3
cites cdi_FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3
container_end_page 228
container_issue A
container_start_page 211
container_title Advances in applied probability
container_volume 50
creator Mitov, Kosto V.
Yanev, Nikolay M.
Hyrien, Ollivier
description In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.
doi_str_mv 10.1017/apr.2018.81
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2187592130</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_apr_2018_81</cupid><sourcerecordid>2187592130</sourcerecordid><originalsourceid>FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3</originalsourceid><addsrcrecordid>eNptkE1LxDAURYMoOI6u_AMFl9LxvaZNMksZP2FEF7oOSZu0GaZNTVpk_r0dZsCNq8eFw72PQ8g1wgIB-Z3qwyIDFAuBJ2SGOS9SBiw_JTMAwFQwLs7JRYybKVIuYEYe3sbt4IZdbxIdVFc2rquTPvjSxGhi8uOGJnFd41tfm874MSYf3sXou8S1rauDGpzvLsmZVdtoro53Tr6eHj9XL-n6_fl1db9OS0rZkFqLWBiWCUaXClmeL3UpQFcKFFO5RW20yBFUxitNsRBWU8gqDbzKbSZ4Sefk5tA7Pfg9mjjIjR9DN03KDAUvlhlSmKjbA1UGH2MwVvbBtSrsJILca5KTJrnXJAVOdHqkVauDq2rzV_of_wuFM2qr</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2187592130</pqid></control><display><type>article</type><title>Multitype branching processes with inhomogeneous Poisson immigration</title><source>ABI/INFORM Global (ProQuest)</source><source>JSTOR Archival Journals and Primary Sources Collection</source><source>Cambridge University Press</source><creator>Mitov, Kosto V. ; Yanev, Nikolay M. ; Hyrien, Ollivier</creator><creatorcontrib>Mitov, Kosto V. ; Yanev, Nikolay M. ; Hyrien, Ollivier</creatorcontrib><description>In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.</description><identifier>ISSN: 0001-8678</identifier><identifier>EISSN: 1475-6064</identifier><identifier>DOI: 10.1017/apr.2018.81</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Asymptotic properties ; Branching (mathematics) ; Fractals ; Immigration ; Markov processes ; Original Article ; Poisson distribution ; Probability</subject><ispartof>Advances in applied probability, 2018-12, Vol.50 (A), p.211-228</ispartof><rights>Copyright © Applied Probability Trust 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3</citedby><cites>FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2187592130?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,11688,27924,27925,36060,44363,72960</link.rule.ids></links><search><creatorcontrib>Mitov, Kosto V.</creatorcontrib><creatorcontrib>Yanev, Nikolay M.</creatorcontrib><creatorcontrib>Hyrien, Ollivier</creatorcontrib><title>Multitype branching processes with inhomogeneous Poisson immigration</title><title>Advances in applied probability</title><addtitle>Adv. Appl. Probab</addtitle><description>In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.</description><subject>Asymptotic properties</subject><subject>Branching (mathematics)</subject><subject>Fractals</subject><subject>Immigration</subject><subject>Markov processes</subject><subject>Original Article</subject><subject>Poisson distribution</subject><subject>Probability</subject><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>M0C</sourceid><recordid>eNptkE1LxDAURYMoOI6u_AMFl9LxvaZNMksZP2FEF7oOSZu0GaZNTVpk_r0dZsCNq8eFw72PQ8g1wgIB-Z3qwyIDFAuBJ2SGOS9SBiw_JTMAwFQwLs7JRYybKVIuYEYe3sbt4IZdbxIdVFc2rquTPvjSxGhi8uOGJnFd41tfm874MSYf3sXou8S1rauDGpzvLsmZVdtoro53Tr6eHj9XL-n6_fl1db9OS0rZkFqLWBiWCUaXClmeL3UpQFcKFFO5RW20yBFUxitNsRBWU8gqDbzKbSZ4Sefk5tA7Pfg9mjjIjR9DN03KDAUvlhlSmKjbA1UGH2MwVvbBtSrsJILca5KTJrnXJAVOdHqkVauDq2rzV_of_wuFM2qr</recordid><startdate>201812</startdate><enddate>201812</enddate><creator>Mitov, Kosto V.</creator><creator>Yanev, Nikolay M.</creator><creator>Hyrien, Ollivier</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>201812</creationdate><title>Multitype branching processes with inhomogeneous Poisson immigration</title><author>Mitov, Kosto V. ; Yanev, Nikolay M. ; Hyrien, Ollivier</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic properties</topic><topic>Branching (mathematics)</topic><topic>Fractals</topic><topic>Immigration</topic><topic>Markov processes</topic><topic>Original Article</topic><topic>Poisson distribution</topic><topic>Probability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mitov, Kosto V.</creatorcontrib><creatorcontrib>Yanev, Nikolay M.</creatorcontrib><creatorcontrib>Hyrien, Ollivier</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest_ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global (ProQuest)</collection><collection>Computing Database</collection><collection>ProQuest_Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Research Library China</collection><collection>Materials science collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Advances in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mitov, Kosto V.</au><au>Yanev, Nikolay M.</au><au>Hyrien, Ollivier</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multitype branching processes with inhomogeneous Poisson immigration</atitle><jtitle>Advances in applied probability</jtitle><addtitle>Adv. Appl. Probab</addtitle><date>2018-12</date><risdate>2018</risdate><volume>50</volume><issue>A</issue><spage>211</spage><epage>228</epage><pages>211-228</pages><issn>0001-8678</issn><eissn>1475-6064</eissn><abstract>In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/apr.2018.81</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0001-8678
ispartof Advances in applied probability, 2018-12, Vol.50 (A), p.211-228
issn 0001-8678
1475-6064
language eng
recordid cdi_proquest_journals_2187592130
source ABI/INFORM Global (ProQuest); JSTOR Archival Journals and Primary Sources Collection; Cambridge University Press
subjects Asymptotic properties
Branching (mathematics)
Fractals
Immigration
Markov processes
Original Article
Poisson distribution
Probability
title Multitype branching processes with inhomogeneous Poisson immigration
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T00%3A40%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Multitype%20branching%20processes%20with%20inhomogeneous%20Poisson%20immigration&rft.jtitle=Advances%20in%20applied%20probability&rft.au=Mitov,%20Kosto%20V.&rft.date=2018-12&rft.volume=50&rft.issue=A&rft.spage=211&rft.epage=228&rft.pages=211-228&rft.issn=0001-8678&rft.eissn=1475-6064&rft_id=info:doi/10.1017/apr.2018.81&rft_dat=%3Cproquest_cross%3E2187592130%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c336t-ff115e628639a16449bc80bda0a6a4f1beb8410a27db3158fb302db07d4f287c3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2187592130&rft_id=info:pmid/&rft_cupid=10_1017_apr_2018_81&rfr_iscdi=true