Loading…
An Application of the Coalescence Theory to Branching Random Walks
In a discrete-time single-type Galton--Watson branching random walk {Z n , ζ n } n≤ 0, where Z n is the population of the nth generation and ζ n is a collection of the positions on ℝ of the Z n individuals in the nth generation, let Y n be the position of a randomly chosen individual from the nth ge...
Saved in:
| Published in: | Journal of applied probability 2013-09, Vol.50 (3), p.893-899 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| 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-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3 |
| container_end_page | 899 |
| container_issue | 3 |
| container_start_page | 893 |
| container_title | Journal of applied probability |
| container_volume | 50 |
| creator | Athreya, K. B. Hong, Jyy-I |
| description | In a discrete-time single-type Galton--Watson branching random walk {Z
n
, ζ
n
}
n≤ 0, where Z
n
is the population of the nth generation and ζ
n
is a collection of the positions on ℝ of the Z
n
individuals in the nth generation, let Y
n
be the position of a randomly chosen individual from the nth generation and Z
n
(x) be the number of points in ζ
n
that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z
1∣ Z
0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 |
| doi_str_mv | 10.1239/jap/1378401245 |
| format | article |
| fullrecord | <record><control><sourceid>jstor_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_jap_1378401245</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1239_jap_1378401245</cupid><jstor_id>43283510</jstor_id><sourcerecordid>43283510</sourcerecordid><originalsourceid>FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3</originalsourceid><addsrcrecordid>eNptkc9LwzAUgIMoOKdXb0LAi5dueU3SNje34S8YCLLhsaRJtrV2TU26w_57oxtT1EsevHzvy3svCF0CGUBMxbCS7RBomjECMeNHqAcs5VFC0vgY9QiJIRLhPEVn3leEAOMi7aHxqMGjtq1LJbvSNtgucLcyeGJlbbwyjTJ4tjLWbXFn8djJRq3KZolfZKPtGr_K-s2fo5OFrL252Mc-mt_fzSaP0fT54WkymkaKJaSLgEIBmhaMS0EhKbKCcq5JnGSScJFopTUXAQUpCi4ACi30IjXMJNQwIIb20e3O2zpbGdWZjapLnbeuXEu3za0s88l8us_uQ9hJ_r2ToLg5KN43xnf5ugxT1rVsjN34HBjL0pSLL_T6F1rZjWvCgIGiDDhNsiRQgx2lnPXemcWhHSD556_87eBqV1D5zroDzWicUQ4k3JO9UK4LV-ql-fHu_8oPyhGXSQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1434153686</pqid></control><display><type>article</type><title>An Application of the Coalescence Theory to Branching Random Walks</title><source>JSTOR</source><creator>Athreya, K. B. ; Hong, Jyy-I</creator><creatorcontrib>Athreya, K. B. ; Hong, Jyy-I</creatorcontrib><description><![CDATA[In a discrete-time single-type Galton--Watson branching random walk {Z
n
, ζ
n
}
n≤ 0, where Z
n
is the population of the nth generation and ζ
n
is a collection of the positions on ℝ of the Z
n
individuals in the nth generation, let Y
n
be the position of a randomly chosen individual from the nth generation and Z
n
(x) be the number of points in ζ
n
that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z
1∣ Z
0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 <α<1, that the sequence of random functions {Z
n
(x)/Z
n
:−∞<x<∞} converges in the finite-dimensional sense to {δ
x
:−∞<x<∞}, where δ
x
≡ 1
{N≤ x} and N is an N(0,1) random variable.]]></description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.1239/jap/1378401245</identifier><identifier>CODEN: JPRBAM</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>60G50 ; 60J80 ; Attraction ; Branching process ; branching random walk ; Central limit theorem ; coalescence ; Coalescing ; Collection ; Cumulative distribution functions ; Explosions ; Explosives ; infinite mean ; Law ; Mathematical functions ; Mathematical theorems ; Perceptron convergence procedure ; Probability distribution ; Random variables ; Random walk ; Random walk theory ; Short Communications ; Studies ; supercritical ; Symbols ; Theoretical mathematics</subject><ispartof>Journal of applied probability, 2013-09, Vol.50 (3), p.893-899</ispartof><rights>Applied Probability Trust</rights><rights>Copyright © 2013 Applied Probability Trust</rights><rights>Copyright Applied Probability Trust Sep 2013</rights><rights>Copyright 2013 Applied Probability Trust</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3</citedby><cites>FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43283510$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/43283510$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,885,27922,27923,58236,58469</link.rule.ids></links><search><creatorcontrib>Athreya, K. B.</creatorcontrib><creatorcontrib>Hong, Jyy-I</creatorcontrib><title>An Application of the Coalescence Theory to Branching Random Walks</title><title>Journal of applied probability</title><addtitle>Journal of Applied Probability</addtitle><description><![CDATA[In a discrete-time single-type Galton--Watson branching random walk {Z
n
, ζ
n
}
n≤ 0, where Z
n
is the population of the nth generation and ζ
n
is a collection of the positions on ℝ of the Z
n
individuals in the nth generation, let Y
n
be the position of a randomly chosen individual from the nth generation and Z
n
(x) be the number of points in ζ
n
that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z
1∣ Z
0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 <α<1, that the sequence of random functions {Z
n
(x)/Z
n
:−∞<x<∞} converges in the finite-dimensional sense to {δ
x
:−∞<x<∞}, where δ
x
≡ 1
{N≤ x} and N is an N(0,1) random variable.]]></description><subject>60G50</subject><subject>60J80</subject><subject>Attraction</subject><subject>Branching process</subject><subject>branching random walk</subject><subject>Central limit theorem</subject><subject>coalescence</subject><subject>Coalescing</subject><subject>Collection</subject><subject>Cumulative distribution functions</subject><subject>Explosions</subject><subject>Explosives</subject><subject>infinite mean</subject><subject>Law</subject><subject>Mathematical functions</subject><subject>Mathematical theorems</subject><subject>Perceptron convergence procedure</subject><subject>Probability distribution</subject><subject>Random variables</subject><subject>Random walk</subject><subject>Random walk theory</subject><subject>Short Communications</subject><subject>Studies</subject><subject>supercritical</subject><subject>Symbols</subject><subject>Theoretical mathematics</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNptkc9LwzAUgIMoOKdXb0LAi5dueU3SNje34S8YCLLhsaRJtrV2TU26w_57oxtT1EsevHzvy3svCF0CGUBMxbCS7RBomjECMeNHqAcs5VFC0vgY9QiJIRLhPEVn3leEAOMi7aHxqMGjtq1LJbvSNtgucLcyeGJlbbwyjTJ4tjLWbXFn8djJRq3KZolfZKPtGr_K-s2fo5OFrL252Mc-mt_fzSaP0fT54WkymkaKJaSLgEIBmhaMS0EhKbKCcq5JnGSScJFopTUXAQUpCi4ACi30IjXMJNQwIIb20e3O2zpbGdWZjapLnbeuXEu3za0s88l8us_uQ9hJ_r2ToLg5KN43xnf5ugxT1rVsjN34HBjL0pSLL_T6F1rZjWvCgIGiDDhNsiRQgx2lnPXemcWhHSD556_87eBqV1D5zroDzWicUQ4k3JO9UK4LV-ql-fHu_8oPyhGXSQ</recordid><startdate>20130901</startdate><enddate>20130901</enddate><creator>Athreya, K. B.</creator><creator>Hong, Jyy-I</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130901</creationdate><title>An Application of the Coalescence Theory to Branching Random Walks</title><author>Athreya, K. B. ; Hong, Jyy-I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>60G50</topic><topic>60J80</topic><topic>Attraction</topic><topic>Branching process</topic><topic>branching random walk</topic><topic>Central limit theorem</topic><topic>coalescence</topic><topic>Coalescing</topic><topic>Collection</topic><topic>Cumulative distribution functions</topic><topic>Explosions</topic><topic>Explosives</topic><topic>infinite mean</topic><topic>Law</topic><topic>Mathematical functions</topic><topic>Mathematical theorems</topic><topic>Perceptron convergence procedure</topic><topic>Probability distribution</topic><topic>Random variables</topic><topic>Random walk</topic><topic>Random walk theory</topic><topic>Short Communications</topic><topic>Studies</topic><topic>supercritical</topic><topic>Symbols</topic><topic>Theoretical mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Athreya, K. B.</creatorcontrib><creatorcontrib>Hong, Jyy-I</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science 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><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Athreya, K. B.</au><au>Hong, Jyy-I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Application of the Coalescence Theory to Branching Random Walks</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>2013-09-01</date><risdate>2013</risdate><volume>50</volume><issue>3</issue><spage>893</spage><epage>899</epage><pages>893-899</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><abstract><![CDATA[In a discrete-time single-type Galton--Watson branching random walk {Z
n
, ζ
n
}
n≤ 0, where Z
n
is the population of the nth generation and ζ
n
is a collection of the positions on ℝ of the Z
n
individuals in the nth generation, let Y
n
be the position of a randomly chosen individual from the nth generation and Z
n
(x) be the number of points in ζ
n
that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z
1∣ Z
0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 <α<1, that the sequence of random functions {Z
n
(x)/Z
n
:−∞<x<∞} converges in the finite-dimensional sense to {δ
x
:−∞<x<∞}, where δ
x
≡ 1
{N≤ x} and N is an N(0,1) random variable.]]></abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1239/jap/1378401245</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 2013-09, Vol.50 (3), p.893-899 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_jap_1378401245 |
| source | JSTOR |
| subjects | 60G50 60J80 Attraction Branching process branching random walk Central limit theorem coalescence Coalescing Collection Cumulative distribution functions Explosions Explosives infinite mean Law Mathematical functions Mathematical theorems Perceptron convergence procedure Probability distribution Random variables Random walk Random walk theory Short Communications Studies supercritical Symbols Theoretical mathematics |
| title | An Application of the Coalescence Theory to Branching Random Walks |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T20%3A04%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20Application%20of%20the%20Coalescence%20Theory%20to%20Branching%20Random%20Walks&rft.jtitle=Journal%20of%20applied%20probability&rft.au=Athreya,%20K.%20B.&rft.date=2013-09-01&rft.volume=50&rft.issue=3&rft.spage=893&rft.epage=899&rft.pages=893-899&rft.issn=0021-9002&rft.eissn=1475-6072&rft.coden=JPRBAM&rft_id=info:doi/10.1239/jap/1378401245&rft_dat=%3Cjstor_proje%3E43283510%3C/jstor_proje%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c460t-131b1d3b45a9316b8b355d0268a0596dcdd59c461a9b5911bd9df7e4e63e410e3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1434153686&rft_id=info:pmid/&rft_cupid=10_1239_jap_1378401245&rft_jstor_id=43283510&rfr_iscdi=true |