KPP equation and supercritical branching brownian motion in the subcritical speed area. Application to spatial trees View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1988-12

AUTHORS

Brigitte Chauvin, Alain Rouault

ABSTRACT

If Rt is the position of the rightmost particle at time t in a one dimensional branching brownian motion, u(t, x)=P(Rt>x) is a solution of KPP equation: where f(u)=α(1-u-g(1-u))g is the generating function of the reproduction law and α the inverse of the mean lifetime; if m=g′(1)>1 and g(0)=0, it is known that: For the general KPP equation, we show limit theorems for u(t, ct+ζ), c>c0, ξ ∈ ℝ, t → +∞. Large deviations for Rt and probabilities of presence of particles for the branching process are deduced: (where Zt denotes the random point measure of particles living at time t) and a Yaglom type theorem is proved. The conditional distribution of the spatial tree, given {Zt(]ct, +∞[)>0}, is studied in the limit as t → +∞. More... »

PAGES

299-314

References to SciGraph publications

  • 1980-01. Brownian first exit from and sojourn over one sided moving boundary and application in PROBABILITY THEORY AND RELATED FIELDS
  • 1979-01. Growth rates in the branching random walk in PROBABILITY THEORY AND RELATED FIELDS
  • 1975. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation in PARTIAL DIFFERENTIAL EQUATIONS AND RELATED TOPICS
  • 1984-05. Rate of expansion of an inhomogeneous branching process of brownian particles in PROBABILITY THEORY AND RELATED FIELDS
  • 1983. Branching Processes in NONE
  • 1979. Mathematical Aspects of Reacting and Diffusing Systems in NONE
  • 1972. Branching Processes in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00356108

    DOI

    http://dx.doi.org/10.1007/bf00356108

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1007486393


    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/2008/0104", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Statistics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "name": [
                "Laboratoire de Probabilit\u00e9s, Universit\u00e9 Paris VI., 4, place Jussieu, tour 56, 3\u00e8me \u00e9tage, F-75230, Paris Cedex 05"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chauvin", 
            "givenName": "Brigitte", 
            "id": "sg:person.015557021304.37", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015557021304.37"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Paris-Sud", 
              "id": "https://www.grid.ac/institutes/grid.5842.b", 
              "name": [
                "UA-CNRS 743, Statistique Appliqu\u00e9e, Universit\u00e9 Paris Sud, Math\u00e9matiques, Bat. 425, F-91405, Orsay Cedex"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rouault", 
            "givenName": "Alain", 
            "id": "sg:person.015632255107.22", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015632255107.22"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1002/cpa.3160310502", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003033067"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160310502", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003033067"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0304-4149(78)90035-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006745532"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1013007979", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4615-8155-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013007979", 
              "https://doi.org/10.1007/978-1-4615-8155-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4615-8155-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013007979", 
              "https://doi.org/10.1007/978-1-4615-8155-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/mana.19821050117", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019546506"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00532800", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024151716", 
              "https://doi.org/10.1007/bf00532800"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00532800", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024151716", 
              "https://doi.org/10.1007/bf00532800"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0001867800022515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030746479"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1034943124", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-65371-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034943124", 
              "https://doi.org/10.1007/978-3-642-65371-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-65371-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034943124", 
              "https://doi.org/10.1007/978-3-642-65371-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0070595", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036244018", 
              "https://doi.org/10.1007/bfb0070595"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-93111-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036634600", 
              "https://doi.org/10.1007/978-3-642-93111-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-93111-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036634600", 
              "https://doi.org/10.1007/978-3-642-93111-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00535355", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040139124", 
              "https://doi.org/10.1007/bf00535355"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00535355", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040139124", 
              "https://doi.org/10.1007/bf00535355"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160280302", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042063001"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160280302", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042063001"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00534879", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043736583", 
              "https://doi.org/10.1007/bf00534879"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00534879", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043736583", 
              "https://doi.org/10.1007/bf00534879"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0021900200104644", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043977314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0021900200025900", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047528569"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1111/j.1469-1809.1937.tb02153.x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049075368"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0304-4149(83)90044-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050179424"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/sm1982v042n03abeh002258", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058200016"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/memo/0285", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059343334"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/aop/1176992901", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064404501"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/1427068", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069490058"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/3213258", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070227450"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/3213469", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070227663"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/kjm/1250522506", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1083509704"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1988-12", 
        "datePublishedReg": "1988-12-01", 
        "description": "If Rt is the position of the rightmost particle at time t in a one dimensional branching brownian motion, u(t, x)=P(Rt>x) is a solution of KPP equation: where f(u)=\u03b1(1-u-g(1-u))g is the generating function of the reproduction law and \u03b1 the inverse of the mean lifetime; if m=g\u2032(1)>1 and g(0)=0, it is known that: For the general KPP equation, we show limit theorems for u(t, ct+\u03b6), c>c0, \u03be \u2208 \u211d, t \u2192 +\u221e. Large deviations for Rt and probabilities of presence of particles for the branching process are deduced: (where Zt denotes the random point measure of particles living at time t) and a Yaglom type theorem is proved. The conditional distribution of the spatial tree, given {Zt(]ct, +\u221e[)>0}, is studied in the limit as t \u2192 +\u221e.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf00356108", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1053886", 
            "issn": [
              "0178-8051", 
              "1432-2064"
            ], 
            "name": "Probability Theory and Related Fields", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "80"
          }
        ], 
        "name": "KPP equation and supercritical branching brownian motion in the subcritical speed area. Application to spatial trees", 
        "pagination": "299-314", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00356108"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "23a89679956f6f8df26dd8dc37d241a986ad62622c5892e383ce8d04feb6dfa2"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1007486393"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00356108", 
          "https://app.dimensions.ai/details/publication/pub.1007486393"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-15T08:54", 
        "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/v90/0000000374_0000000374/records_119752_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF00356108"
      }
    ]
     

    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/bf00356108'

    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/bf00356108'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00356108'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00356108'


     

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

    150 TRIPLES      21 PREDICATES      52 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00356108 schema:about anzsrc-for:01
    2 anzsrc-for:0104
    3 schema:author N1ecb84ef3254492ab8719a3cb6e560ee
    4 schema:citation sg:pub.10.1007/978-1-4615-8155-0
    5 sg:pub.10.1007/978-3-642-65371-1
    6 sg:pub.10.1007/978-3-642-93111-6
    7 sg:pub.10.1007/bf00532800
    8 sg:pub.10.1007/bf00534879
    9 sg:pub.10.1007/bf00535355
    10 sg:pub.10.1007/bfb0070595
    11 https://app.dimensions.ai/details/publication/pub.1013007979
    12 https://app.dimensions.ai/details/publication/pub.1034943124
    13 https://doi.org/10.1002/cpa.3160280302
    14 https://doi.org/10.1002/cpa.3160310502
    15 https://doi.org/10.1002/mana.19821050117
    16 https://doi.org/10.1016/0304-4149(78)90035-2
    17 https://doi.org/10.1016/0304-4149(83)90044-3
    18 https://doi.org/10.1017/s0001867800022515
    19 https://doi.org/10.1017/s0021900200025900
    20 https://doi.org/10.1017/s0021900200104644
    21 https://doi.org/10.1070/sm1982v042n03abeh002258
    22 https://doi.org/10.1090/memo/0285
    23 https://doi.org/10.1111/j.1469-1809.1937.tb02153.x
    24 https://doi.org/10.1214/aop/1176992901
    25 https://doi.org/10.1215/kjm/1250522506
    26 https://doi.org/10.2307/1427068
    27 https://doi.org/10.2307/3213258
    28 https://doi.org/10.2307/3213469
    29 schema:datePublished 1988-12
    30 schema:datePublishedReg 1988-12-01
    31 schema:description If Rt is the position of the rightmost particle at time t in a one dimensional branching brownian motion, u(t, x)=P(Rt>x) is a solution of KPP equation: where f(u)=α(1-u-g(1-u))g is the generating function of the reproduction law and α the inverse of the mean lifetime; if m=g′(1)>1 and g(0)=0, it is known that: For the general KPP equation, we show limit theorems for u(t, ct+ζ), c>c0, ξ ∈ ℝ, t → +∞. Large deviations for Rt and probabilities of presence of particles for the branching process are deduced: (where Zt denotes the random point measure of particles living at time t) and a Yaglom type theorem is proved. The conditional distribution of the spatial tree, given {Zt(]ct, +∞[)>0}, is studied in the limit as t → +∞.
    32 schema:genre research_article
    33 schema:inLanguage en
    34 schema:isAccessibleForFree false
    35 schema:isPartOf N9d8ea8785886421ba34f7646220a821a
    36 Nf296090c495c4988a86e3864bd8e650a
    37 sg:journal.1053886
    38 schema:name KPP equation and supercritical branching brownian motion in the subcritical speed area. Application to spatial trees
    39 schema:pagination 299-314
    40 schema:productId N1f5db3dbe798414b9a42b423d25bd7ee
    41 N220407b0eee547059b8928afe58e02e1
    42 N4aafb4ff66004dfa9239c1ac1d80679c
    43 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007486393
    44 https://doi.org/10.1007/bf00356108
    45 schema:sdDatePublished 2019-04-15T08:54
    46 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    47 schema:sdPublisher N443313f389524f82ae6b7fbefef67f2a
    48 schema:url http://link.springer.com/10.1007/BF00356108
    49 sgo:license sg:explorer/license/
    50 sgo:sdDataset articles
    51 rdf:type schema:ScholarlyArticle
    52 N1ecb84ef3254492ab8719a3cb6e560ee rdf:first sg:person.015557021304.37
    53 rdf:rest Ndcece68af80b44b586da9a7376854969
    54 N1f5db3dbe798414b9a42b423d25bd7ee schema:name dimensions_id
    55 schema:value pub.1007486393
    56 rdf:type schema:PropertyValue
    57 N220407b0eee547059b8928afe58e02e1 schema:name doi
    58 schema:value 10.1007/bf00356108
    59 rdf:type schema:PropertyValue
    60 N443313f389524f82ae6b7fbefef67f2a schema:name Springer Nature - SN SciGraph project
    61 rdf:type schema:Organization
    62 N4aafb4ff66004dfa9239c1ac1d80679c schema:name readcube_id
    63 schema:value 23a89679956f6f8df26dd8dc37d241a986ad62622c5892e383ce8d04feb6dfa2
    64 rdf:type schema:PropertyValue
    65 N9d8ea8785886421ba34f7646220a821a schema:volumeNumber 80
    66 rdf:type schema:PublicationVolume
    67 Ndcece68af80b44b586da9a7376854969 rdf:first sg:person.015632255107.22
    68 rdf:rest rdf:nil
    69 Nde45bd8edc3649c58e29c29f62012040 schema:name Laboratoire de Probabilités, Université Paris VI., 4, place Jussieu, tour 56, 3ème étage, F-75230, Paris Cedex 05
    70 rdf:type schema:Organization
    71 Nf296090c495c4988a86e3864bd8e650a schema:issueNumber 2
    72 rdf:type schema:PublicationIssue
    73 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    74 schema:name Mathematical Sciences
    75 rdf:type schema:DefinedTerm
    76 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
    77 schema:name Statistics
    78 rdf:type schema:DefinedTerm
    79 sg:journal.1053886 schema:issn 0178-8051
    80 1432-2064
    81 schema:name Probability Theory and Related Fields
    82 rdf:type schema:Periodical
    83 sg:person.015557021304.37 schema:affiliation Nde45bd8edc3649c58e29c29f62012040
    84 schema:familyName Chauvin
    85 schema:givenName Brigitte
    86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015557021304.37
    87 rdf:type schema:Person
    88 sg:person.015632255107.22 schema:affiliation https://www.grid.ac/institutes/grid.5842.b
    89 schema:familyName Rouault
    90 schema:givenName Alain
    91 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015632255107.22
    92 rdf:type schema:Person
    93 sg:pub.10.1007/978-1-4615-8155-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013007979
    94 https://doi.org/10.1007/978-1-4615-8155-0
    95 rdf:type schema:CreativeWork
    96 sg:pub.10.1007/978-3-642-65371-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034943124
    97 https://doi.org/10.1007/978-3-642-65371-1
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/978-3-642-93111-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036634600
    100 https://doi.org/10.1007/978-3-642-93111-6
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/bf00532800 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024151716
    103 https://doi.org/10.1007/bf00532800
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/bf00534879 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043736583
    106 https://doi.org/10.1007/bf00534879
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/bf00535355 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040139124
    109 https://doi.org/10.1007/bf00535355
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/bfb0070595 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036244018
    112 https://doi.org/10.1007/bfb0070595
    113 rdf:type schema:CreativeWork
    114 https://app.dimensions.ai/details/publication/pub.1013007979 schema:CreativeWork
    115 https://app.dimensions.ai/details/publication/pub.1034943124 schema:CreativeWork
    116 https://doi.org/10.1002/cpa.3160280302 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042063001
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1002/cpa.3160310502 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003033067
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1002/mana.19821050117 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019546506
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1016/0304-4149(78)90035-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006745532
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1016/0304-4149(83)90044-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050179424
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.1017/s0001867800022515 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030746479
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.1017/s0021900200025900 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047528569
    129 rdf:type schema:CreativeWork
    130 https://doi.org/10.1017/s0021900200104644 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043977314
    131 rdf:type schema:CreativeWork
    132 https://doi.org/10.1070/sm1982v042n03abeh002258 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058200016
    133 rdf:type schema:CreativeWork
    134 https://doi.org/10.1090/memo/0285 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059343334
    135 rdf:type schema:CreativeWork
    136 https://doi.org/10.1111/j.1469-1809.1937.tb02153.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1049075368
    137 rdf:type schema:CreativeWork
    138 https://doi.org/10.1214/aop/1176992901 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064404501
    139 rdf:type schema:CreativeWork
    140 https://doi.org/10.1215/kjm/1250522506 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083509704
    141 rdf:type schema:CreativeWork
    142 https://doi.org/10.2307/1427068 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069490058
    143 rdf:type schema:CreativeWork
    144 https://doi.org/10.2307/3213258 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070227450
    145 rdf:type schema:CreativeWork
    146 https://doi.org/10.2307/3213469 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070227663
    147 rdf:type schema:CreativeWork
    148 https://www.grid.ac/institutes/grid.5842.b schema:alternateName University of Paris-Sud
    149 schema:name UA-CNRS 743, Statistique Appliquée, Université Paris Sud, Mathématiques, Bat. 425, F-91405, Orsay Cedex
    150 rdf:type schema:Organization
     




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


    ...