The Critical Galton-Watson Process Without Further Power Moments
In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process {Z n ; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, whi...
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| Veröffentlicht in: | Journal of applied probability 2007-09, Vol.44 (3), p.753-769 |
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| container_title | Journal of applied probability |
| container_volume | 44 |
| creator | Nagaev, S. V. Wachtel, V. |
| description | In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process {Z
n
; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, which gives an exponential limit. We also give an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability. |
| doi_str_mv | 10.1239/jap/1189717543 |
| format | Article |
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n
; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, which gives an exponential limit. We also give an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability.</description><subject>60F05</subject><subject>60J80</subject><subject>Asymptotic methods</subject><subject>conditional theorem</subject><subject>Critical Galton-Watson process</subject><subject>Distribution functions</subject><subject>Generating function</subject><subject>Logarithms</subject><subject>Mathematical functions</subject><subject>Mathematical theorems</subject><subject>Probability</subject><subject>Random variables</subject><subject>slowly varying function</subject><subject>Stochastic models</subject><subject>Studies</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kM1Lw0AQxRdRsFav3oTgPe1-ZndvlWCrULGHlh7DZrOxCWm27m4Q_3sjDe1BvMzAzJvfGx4A9whOECZyWqvDFCEhOeKMkgswQpSzOIEcX4IRhBjFsq_X4Mb7GkJEmeQjMFvvTJS6KlRaNdFCNcG28VYFb9to5aw23kfbKuxsF6J558LOuGhlv_r6ZvemDf4WXJWq8eZu6GOwmT-v05d4-b54TZ-WsaY4CTGjAmNWCqMFx7lMuCwQTUghYZKXBEGFNE6wkYLkkOY5K4tCUExwrhgtcFKSMZgduQdna6OD6XRTFdnBVXvlvjOrqizdLIfp0PpEsnMiPeLxhPjsjA9ZbTvX9l9nmFAJsWCyF02OIu2s986UJwsEs9-c_1Ifjge1D9ad1JgzyYSA_R4OQLXPXVV8mLPtP8gf36eJHQ</recordid><startdate>20070901</startdate><enddate>20070901</enddate><creator>Nagaev, S. V.</creator><creator>Wachtel, V.</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>20070901</creationdate><title>The Critical Galton-Watson Process Without Further Power Moments</title><author>Nagaev, S. V. ; Wachtel, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c426t-548225f8ec872b9679d1463d906bf310a1c262e983b04bb5fdd84232ba54d26f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>60F05</topic><topic>60J80</topic><topic>Asymptotic methods</topic><topic>conditional theorem</topic><topic>Critical Galton-Watson process</topic><topic>Distribution functions</topic><topic>Generating function</topic><topic>Logarithms</topic><topic>Mathematical functions</topic><topic>Mathematical theorems</topic><topic>Probability</topic><topic>Random variables</topic><topic>slowly varying function</topic><topic>Stochastic models</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nagaev, S. V.</creatorcontrib><creatorcontrib>Wachtel, V.</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>Nagaev, S. V.</au><au>Wachtel, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Critical Galton-Watson Process Without Further Power Moments</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>2007-09-01</date><risdate>2007</risdate><volume>44</volume><issue>3</issue><spage>753</spage><epage>769</epage><pages>753-769</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><abstract>In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process {Z
n
; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, which gives an exponential limit. We also give an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1239/jap/1189717543</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Cambridge Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | 60F05 60J80 Asymptotic methods conditional theorem Critical Galton-Watson process Distribution functions Generating function Logarithms Mathematical functions Mathematical theorems Probability Random variables slowly varying function Stochastic models Studies |
| title | The Critical Galton-Watson Process Without Further Power Moments |
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