On Times to Quasi-stationarity for Birth and Death Processes View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-09

AUTHORS

Persi Diaconis, Laurent Miclo

ABSTRACT

The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of “local equilibria.” More... »

PAGES

558-586

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10959-009-0234-6

DOI

http://dx.doi.org/10.1007/s10959-009-0234-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031391876


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Artificial Intelligence and Image Processing", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Nice Sophia Antipolis University", 
          "id": "https://www.grid.ac/institutes/grid.10737.32", 
          "name": [
            "Department of Mathematics and Statistics, Stanford University, Stanford, USA", 
            "CNRS, Universit\u00e9 de Nice-Sophia Antipolis, Nice, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Diaconis", 
        "givenName": "Persi", 
        "id": "sg:person.01325567224.91", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01325567224.91"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "French National Centre for Scientific Research", 
          "id": "https://www.grid.ac/institutes/grid.4444.0", 
          "name": [
            "Laboratoire d\u2019Analyse, Topologie, Probabilit\u00e9s, Centre de Math\u00e9matiques et Informatique, Universit\u00e9 de Provence, 39, rue Fr\u00e9d\u00e9ric Joliot-Curie, 13453, Marseille cedex 13, France", 
            "C.N.R.S., Marseille, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Miclo", 
        "givenName": "Laurent", 
        "id": "sg:person.010735732537.44", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010735732537.44"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1017/cbo9780511662430.009", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002503603"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10959-009-0233-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004292409", 
          "https://doi.org/10.1007/s10959-009-0233-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10959-009-0233-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004292409", 
          "https://doi.org/10.1007/s10959-009-0233-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10959-009-0235-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005057902", 
          "https://doi.org/10.1007/s10959-009-0235-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10959-009-0235-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005057902", 
          "https://doi.org/10.1007/s10959-009-0235-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0196-8858(87)90006-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020215903"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01046778", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032757696", 
          "https://doi.org/10.1007/bf01046778"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01046778", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032757696", 
          "https://doi.org/10.1007/bf01046778"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-6200-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038147227", 
          "https://doi.org/10.1007/978-1-4612-6200-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-6200-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038147227", 
          "https://doi.org/10.1007/978-1-4612-6200-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002200200609", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038453930", 
          "https://doi.org/10.1007/s002200200609"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0024-3795(79)90098-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040942676"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1041911968", 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1041911968", 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/105051606000000501", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064391920"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aoap/1035463326", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064397754"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aop/1176990628", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064403953"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aop/1176993924", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064404854"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aop/1176994363", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064404899"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/pjm.1959.9.1109", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069062704"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2304386", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069874054"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2323590", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069888675"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/3211909", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070226149"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/3214809", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070228961"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4171/rmi/241", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072320526"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/dimacs/041", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1097022574"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00029890.1986.11971821", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1100796826"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00029890.1947.11990189", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1103202071"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2009-09", 
    "datePublishedReg": "2009-09-01", 
    "description": "The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of \u201clocal equilibria.\u201d", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10959-009-0234-6", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136853", 
        "issn": [
          "0894-9840", 
          "1572-9230"
        ], 
        "name": "Journal of Theoretical Probability", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "22"
      }
    ], 
    "name": "On Times to Quasi-stationarity for Birth and Death Processes", 
    "pagination": "558-586", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "958b6bfe81c3eb99a9283ee57c2900380bff77f9e3f24b10759e65a95458410b"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10959-009-0234-6"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1031391876"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10959-009-0234-6", 
      "https://app.dimensions.ai/details/publication/pub.1031391876"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T09:17", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000339_0000000339/records_109480_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs10959-009-0234-6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10959-009-0234-6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10959-009-0234-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10959-009-0234-6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10959-009-0234-6'


 

This table displays all metadata directly associated to this object as RDF triples.

146 TRIPLES      21 PREDICATES      50 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10959-009-0234-6 schema:about anzsrc-for:08
2 anzsrc-for:0801
3 schema:author N036a621139924ddfb9473e1057fba682
4 schema:citation sg:pub.10.1007/978-1-4612-6200-8
5 sg:pub.10.1007/bf01046778
6 sg:pub.10.1007/s002200200609
7 sg:pub.10.1007/s10959-009-0233-7
8 sg:pub.10.1007/s10959-009-0235-5
9 https://app.dimensions.ai/details/publication/pub.1041911968
10 https://doi.org/10.1016/0024-3795(79)90098-3
11 https://doi.org/10.1016/0196-8858(87)90006-6
12 https://doi.org/10.1017/cbo9780511662430.009
13 https://doi.org/10.1080/00029890.1947.11990189
14 https://doi.org/10.1080/00029890.1986.11971821
15 https://doi.org/10.1090/dimacs/041
16 https://doi.org/10.1214/105051606000000501
17 https://doi.org/10.1214/aoap/1035463326
18 https://doi.org/10.1214/aop/1176990628
19 https://doi.org/10.1214/aop/1176993924
20 https://doi.org/10.1214/aop/1176994363
21 https://doi.org/10.2140/pjm.1959.9.1109
22 https://doi.org/10.2307/2304386
23 https://doi.org/10.2307/2323590
24 https://doi.org/10.2307/3211909
25 https://doi.org/10.2307/3214809
26 https://doi.org/10.4171/rmi/241
27 schema:datePublished 2009-09
28 schema:datePublishedReg 2009-09-01
29 schema:description The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of “local equilibria.”
30 schema:genre research_article
31 schema:inLanguage en
32 schema:isAccessibleForFree true
33 schema:isPartOf N117cb4ef9188410c84b3078d31d9ac86
34 Nbf8cd07061404e2e81f794ecfaedb765
35 sg:journal.1136853
36 schema:name On Times to Quasi-stationarity for Birth and Death Processes
37 schema:pagination 558-586
38 schema:productId N520ca1da50bd46a588d9ee69028d47a6
39 N71cf9aa0a59241a5b71c9cb93d387a76
40 Nf472af9146b545ef9bf8e557fa2e1ca0
41 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031391876
42 https://doi.org/10.1007/s10959-009-0234-6
43 schema:sdDatePublished 2019-04-11T09:17
44 schema:sdLicense https://scigraph.springernature.com/explorer/license/
45 schema:sdPublisher N57316e667f514f02a4603c86c71ff239
46 schema:url http://link.springer.com/10.1007%2Fs10959-009-0234-6
47 sgo:license sg:explorer/license/
48 sgo:sdDataset articles
49 rdf:type schema:ScholarlyArticle
50 N036a621139924ddfb9473e1057fba682 rdf:first sg:person.01325567224.91
51 rdf:rest N7cdfa5c16ec246c4bf9dc6027b043e32
52 N117cb4ef9188410c84b3078d31d9ac86 schema:volumeNumber 22
53 rdf:type schema:PublicationVolume
54 N520ca1da50bd46a588d9ee69028d47a6 schema:name doi
55 schema:value 10.1007/s10959-009-0234-6
56 rdf:type schema:PropertyValue
57 N57316e667f514f02a4603c86c71ff239 schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 N71cf9aa0a59241a5b71c9cb93d387a76 schema:name dimensions_id
60 schema:value pub.1031391876
61 rdf:type schema:PropertyValue
62 N7cdfa5c16ec246c4bf9dc6027b043e32 rdf:first sg:person.010735732537.44
63 rdf:rest rdf:nil
64 Nbf8cd07061404e2e81f794ecfaedb765 schema:issueNumber 3
65 rdf:type schema:PublicationIssue
66 Nf472af9146b545ef9bf8e557fa2e1ca0 schema:name readcube_id
67 schema:value 958b6bfe81c3eb99a9283ee57c2900380bff77f9e3f24b10759e65a95458410b
68 rdf:type schema:PropertyValue
69 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
70 schema:name Information and Computing Sciences
71 rdf:type schema:DefinedTerm
72 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
73 schema:name Artificial Intelligence and Image Processing
74 rdf:type schema:DefinedTerm
75 sg:journal.1136853 schema:issn 0894-9840
76 1572-9230
77 schema:name Journal of Theoretical Probability
78 rdf:type schema:Periodical
79 sg:person.010735732537.44 schema:affiliation https://www.grid.ac/institutes/grid.4444.0
80 schema:familyName Miclo
81 schema:givenName Laurent
82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010735732537.44
83 rdf:type schema:Person
84 sg:person.01325567224.91 schema:affiliation https://www.grid.ac/institutes/grid.10737.32
85 schema:familyName Diaconis
86 schema:givenName Persi
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01325567224.91
88 rdf:type schema:Person
89 sg:pub.10.1007/978-1-4612-6200-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038147227
90 https://doi.org/10.1007/978-1-4612-6200-8
91 rdf:type schema:CreativeWork
92 sg:pub.10.1007/bf01046778 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032757696
93 https://doi.org/10.1007/bf01046778
94 rdf:type schema:CreativeWork
95 sg:pub.10.1007/s002200200609 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038453930
96 https://doi.org/10.1007/s002200200609
97 rdf:type schema:CreativeWork
98 sg:pub.10.1007/s10959-009-0233-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004292409
99 https://doi.org/10.1007/s10959-009-0233-7
100 rdf:type schema:CreativeWork
101 sg:pub.10.1007/s10959-009-0235-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005057902
102 https://doi.org/10.1007/s10959-009-0235-5
103 rdf:type schema:CreativeWork
104 https://app.dimensions.ai/details/publication/pub.1041911968 schema:CreativeWork
105 https://doi.org/10.1016/0024-3795(79)90098-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040942676
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/0196-8858(87)90006-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020215903
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1017/cbo9780511662430.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002503603
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1080/00029890.1947.11990189 schema:sameAs https://app.dimensions.ai/details/publication/pub.1103202071
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1080/00029890.1986.11971821 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100796826
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1090/dimacs/041 schema:sameAs https://app.dimensions.ai/details/publication/pub.1097022574
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1214/105051606000000501 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064391920
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1214/aoap/1035463326 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064397754
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1214/aop/1176990628 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064403953
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1214/aop/1176993924 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064404854
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1214/aop/1176994363 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064404899
126 rdf:type schema:CreativeWork
127 https://doi.org/10.2140/pjm.1959.9.1109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069062704
128 rdf:type schema:CreativeWork
129 https://doi.org/10.2307/2304386 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069874054
130 rdf:type schema:CreativeWork
131 https://doi.org/10.2307/2323590 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069888675
132 rdf:type schema:CreativeWork
133 https://doi.org/10.2307/3211909 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070226149
134 rdf:type schema:CreativeWork
135 https://doi.org/10.2307/3214809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070228961
136 rdf:type schema:CreativeWork
137 https://doi.org/10.4171/rmi/241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072320526
138 rdf:type schema:CreativeWork
139 https://www.grid.ac/institutes/grid.10737.32 schema:alternateName Nice Sophia Antipolis University
140 schema:name CNRS, Université de Nice-Sophia Antipolis, Nice, France
141 Department of Mathematics and Statistics, Stanford University, Stanford, USA
142 rdf:type schema:Organization
143 https://www.grid.ac/institutes/grid.4444.0 schema:alternateName French National Centre for Scientific Research
144 schema:name C.N.R.S., Marseille, France
145 Laboratoire d’Analyse, Topologie, Probabilités, Centre de Mathématiques et Informatique, Université de Provence, 39, rue Frédéric Joliot-Curie, 13453, Marseille cedex 13, France
146 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...