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Central Limit Analogues for Markov Population Processes
It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein-Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form.
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| Published in: | Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1973-01, Vol.35 (1), p.1-23 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c3008-d02e3859486026be829cfa366c34f3d5bddb61485265b307dd13dba77f670a533 |
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| cites | cdi_FETCH-LOGICAL-c3008-d02e3859486026be829cfa366c34f3d5bddb61485265b307dd13dba77f670a533 |
| container_end_page | 23 |
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Journal of the Royal Statistical Society. Series B, Methodological |
| container_volume | 35 |
| creator | McNeil, Donald R. Schach, Siegfried |
| description | It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein-Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form. |
| doi_str_mv | 10.1111/j.2517-6161.1973.tb00928.x |
| format | article |
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Schach, Siegfried</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3008-d02e3859486026be829cfa366c34f3d5bddb61485265b307dd13dba77f670a533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1973</creationdate><topic>Approximation</topic><topic>birth and death processes</topic><topic>convergence of markov processes</topic><topic>Determinism</topic><topic>markov population models</topic><topic>Markov processes</topic><topic>Mortality</topic><topic>Ornstein Uhlenbeck process</topic><topic>ornstein‐uhlenbeck processes</topic><topic>Perceptron convergence procedure</topic><topic>Population growth</topic><topic>Population size</topic><topic>Stochastic processes</topic><topic>Transition probabilities</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>McNeil, Donald R.</creatorcontrib><creatorcontrib>Schach, Siegfried</creatorcontrib><collection>CrossRef</collection><collection>Periodicals Index Online Segment 18</collection><collection>Periodicals Index Online Segment 32</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>McNeil, Donald R.</au><au>Schach, Siegfried</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Central Limit Analogues for Markov Population Processes</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle><date>1973-01-01</date><risdate>1973</risdate><volume>35</volume><issue>1</issue><spage>1</spage><epage>23</epage><pages>1-23</pages><issn>0035-9246</issn><issn>1369-7412</issn><eissn>2517-6161</eissn><eissn>1467-9868</eissn><abstract>It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein-Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form.</abstract><cop>London</cop><pub>Royal Statistical Society</pub><doi>10.1111/j.2517-6161.1973.tb00928.x</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0035-9246 |
| ispartof | Journal of the Royal Statistical Society. Series B, Methodological, 1973-01, Vol.35 (1), p.1-23 |
| issn | 0035-9246 1369-7412 2517-6161 1467-9868 |
| language | eng |
| recordid | cdi_proquest_journals_1302937386 |
| source | JSTOR Archival Journals and Primary Sources Collection |
| subjects | Approximation birth and death processes convergence of markov processes Determinism markov population models Markov processes Mortality Ornstein Uhlenbeck process ornstein‐uhlenbeck processes Perceptron convergence procedure Population growth Population size Stochastic processes Transition probabilities |
| title | Central Limit Analogues for Markov Population Processes |
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