Extended continued fractions, recurrence relations and two-dimensional Markov processes
Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended conti...
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| Veröffentlicht in: | Advances in applied probability 1989-06, Vol.21 (2), p.357-375 |
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| container_end_page | 375 |
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| container_title | Advances in applied probability |
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| creator | Pearce, C. E. M. |
| description | Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic. |
| doi_str_mv | 10.2307/1427164 |
| format | Article |
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E. M.</creatorcontrib><title>Extended continued fractions, recurrence relations and two-dimensional Markov processes</title><title>Advances in applied probability</title><addtitle>Advances in Applied Probability</addtitle><description>Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.</description><subject>Coefficients</subject><subject>Continued fractions</subject><subject>Differential equations</subject><subject>Equations</subject><subject>Exact sciences and technology</subject><subject>Generating function</subject><subject>Integers</subject><subject>Markov processes</subject><subject>Mathematics</subject><subject>Power series</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Radii of convergence</subject><subject>Recurrence relations</subject><subject>Sciences and techniques of general use</subject><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEQx4MoWKv4FfagiOBqXk02Ryn1AYoXxeOSTWZl6zYpma2Pb2-0BQ-Cp5n5z495_Ak5ZPScC6ovmOSaKblFRkzqSamokttkRCllZaV0tUv2EOe5FLqiI_I8-xggePCFi2HowipnbbJu6GLAsyKBW6UEwUFOe_ujFjb4YniPpe8WEDBLti_ubXqNb8UyRQeIgPtkp7U9wsEmjsnT1exxelPePVzfTi_vSieYHEpmWgX5Ku-BeUVZK7xzbGKct8wwBQC-odpzb4zhrW009w2TglMtcstwMSYn67kuRcQEbb1M3cKmz5rR-tuPeuNHJo_X5NKis31-MrgOf3Gjq4nUNHNHa26OQ0z_jDvdLLaLJnX-Bep5XKXsBf5hvwD60nli</recordid><startdate>19890601</startdate><enddate>19890601</enddate><creator>Pearce, C. E. M.</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19890601</creationdate><title>Extended continued fractions, recurrence relations and two-dimensional Markov processes</title><author>Pearce, C. E. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-19f6e678dde1d601f3dcc159cda1916eeedb07d2d9992fab72db1432073eed923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>Coefficients</topic><topic>Continued fractions</topic><topic>Differential equations</topic><topic>Equations</topic><topic>Exact sciences and technology</topic><topic>Generating function</topic><topic>Integers</topic><topic>Markov processes</topic><topic>Mathematics</topic><topic>Power series</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Radii of convergence</topic><topic>Recurrence relations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pearce, C. E. M.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Advances in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pearce, C. E. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extended continued fractions, recurrence relations and two-dimensional Markov processes</atitle><jtitle>Advances in applied probability</jtitle><addtitle>Advances in Applied Probability</addtitle><date>1989-06-01</date><risdate>1989</risdate><volume>21</volume><issue>2</issue><spage>357</spage><epage>375</epage><pages>357-375</pages><issn>0001-8678</issn><eissn>1475-6064</eissn><coden>AAPBBD</coden><abstract>Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.2307/1427164</doi><tpages>19</tpages></addata></record> |
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| ispartof | Advances in applied probability, 1989-06, Vol.21 (2), p.357-375 |
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| language | eng |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Coefficients Continued fractions Differential equations Equations Exact sciences and technology Generating function Integers Markov processes Mathematics Power series Probability and statistics Probability theory and stochastic processes Radii of convergence Recurrence relations Sciences and techniques of general use |
| title | Extended continued fractions, recurrence relations and two-dimensional Markov processes |
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