Limiting Distributions in Branching Processes with Two Types of Particles View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

1997

AUTHORS

Michael Drmota , Vladimir Vatutin

ABSTRACT

Let us consider a decomposable e branching process with two types of particles T1, T2 such that particles of type T2 can only produce particles of types T1 whereas particles of type T1 can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T1 and T2 when the total number n of all particles is fixed. Especially we are interested in the limit case n — ∞. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x2 distributions, appear. More... »

PAGES

89-110

Book

TITLE

Classical and Modern Branching Processes

ISBN

978-1-4612-7315-8
978-1-4612-1862-3

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4612-1862-3_7

DOI

http://dx.doi.org/10.1007/978-1-4612-1862-3_7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046846421


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/2008/0904", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Chemical Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "TU Wien", 
          "id": "https://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Department of Discrete Mathematics, Technical University of Vienna, Wiedner Hauptstra\u00dfe 8-10/118, A-1040, Vienna, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Drmota", 
        "givenName": "Michael", 
        "id": "sg:person.011120311545.44", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011120311545.44"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Steklov Mathematical Institute", 
          "id": "https://www.grid.ac/institutes/grid.426543.2", 
          "name": [
            "Steklov Mathematical Institute, 42 Vavilov Street, 117 966, Moscow, GSP-1, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Vatutin", 
        "givenName": "Vladimir", 
        "id": "sg:person.011756451263.50", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011756451263.50"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1515/dma.1994.4.1.45", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003202694"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/eujc.1994.1016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035948447"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0097-3165(73)90038-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042257341"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0097-3165(94)90011-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050240691"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0403019", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062844610"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1997", 
    "datePublishedReg": "1997-01-01", 
    "description": "Let us consider a decomposable e branching process with two types of particles T1, T2 such that particles of type T2 can only produce particles of types T1 whereas particles of type T1 can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T1 and T2 when the total number n of all particles is fixed. Especially we are interested in the limit case n \u2014 \u221e. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x2 distributions, appear.", 
    "editor": [
      {
        "familyName": "Athreya", 
        "givenName": "Krishna B.", 
        "type": "Person"
      }, 
      {
        "familyName": "Jagers", 
        "givenName": "Peter", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4612-1862-3_7", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-1-4612-7315-8", 
        "978-1-4612-1862-3"
      ], 
      "name": "Classical and Modern Branching Processes", 
      "type": "Book"
    }, 
    "name": "Limiting Distributions in Branching Processes with Two Types of Particles", 
    "pagination": "89-110", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1046846421"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4612-1862-3_7"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "df28a1767b592cb84afa470e4561d867e9f5a72d60ae25d41707c01f27cf8bcb"
        ]
      }
    ], 
    "publisher": {
      "location": "New York, NY", 
      "name": "Springer New York", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4612-1862-3_7", 
      "https://app.dimensions.ai/details/publication/pub.1046846421"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T08:59", 
    "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/v90/0000000369_0000000369/records_68984_00000001.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-1-4612-1862-3_7"
  }
]
 

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.10.1007/978-1-4612-1862-3_7'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1862-3_7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1862-3_7'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4612-1862-3_7'


 

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

95 TRIPLES      23 PREDICATES      32 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4612-1862-3_7 schema:about anzsrc-for:09
2 anzsrc-for:0904
3 schema:author N8f03f97a4c484bbf974d34e50f280e40
4 schema:citation https://doi.org/10.1006/eujc.1994.1016
5 https://doi.org/10.1016/0097-3165(73)90038-1
6 https://doi.org/10.1016/0097-3165(94)90011-6
7 https://doi.org/10.1137/0403019
8 https://doi.org/10.1515/dma.1994.4.1.45
9 schema:datePublished 1997
10 schema:datePublishedReg 1997-01-01
11 schema:description Let us consider a decomposable e branching process with two types of particles T1, T2 such that particles of type T2 can only produce particles of types T1 whereas particles of type T1 can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T1 and T2 when the total number n of all particles is fixed. Especially we are interested in the limit case n — ∞. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x2 distributions, appear.
12 schema:editor N527245a3093a40a29ff52be3dca562d4
13 schema:genre chapter
14 schema:inLanguage en
15 schema:isAccessibleForFree true
16 schema:isPartOf N1c747e9823e54ad58cf415d93fac28e9
17 schema:name Limiting Distributions in Branching Processes with Two Types of Particles
18 schema:pagination 89-110
19 schema:productId N223b48112e9049de9aa2dbb231776490
20 Nb285e57673b34553a5f2de9e0d8e0e87
21 Nbc545c351c744c2f95face4e16e4cd2b
22 schema:publisher Nc85103ffce2a43ea9f382405f2f805f5
23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046846421
24 https://doi.org/10.1007/978-1-4612-1862-3_7
25 schema:sdDatePublished 2019-04-16T08:59
26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
27 schema:sdPublisher Ne5d6b1b3cb4842c4b2c7a160a770b67d
28 schema:url https://link.springer.com/10.1007%2F978-1-4612-1862-3_7
29 sgo:license sg:explorer/license/
30 sgo:sdDataset chapters
31 rdf:type schema:Chapter
32 N1c747e9823e54ad58cf415d93fac28e9 schema:isbn 978-1-4612-1862-3
33 978-1-4612-7315-8
34 schema:name Classical and Modern Branching Processes
35 rdf:type schema:Book
36 N223b48112e9049de9aa2dbb231776490 schema:name dimensions_id
37 schema:value pub.1046846421
38 rdf:type schema:PropertyValue
39 N2bc643ad25544261bfad905b461dc64c schema:familyName Athreya
40 schema:givenName Krishna B.
41 rdf:type schema:Person
42 N35cb782975a64a48800c06cdeb074c8b rdf:first sg:person.011756451263.50
43 rdf:rest rdf:nil
44 N527245a3093a40a29ff52be3dca562d4 rdf:first N2bc643ad25544261bfad905b461dc64c
45 rdf:rest Nf791adc61efe42b1bf1daa6acff86217
46 N8f03f97a4c484bbf974d34e50f280e40 rdf:first sg:person.011120311545.44
47 rdf:rest N35cb782975a64a48800c06cdeb074c8b
48 Nb285e57673b34553a5f2de9e0d8e0e87 schema:name doi
49 schema:value 10.1007/978-1-4612-1862-3_7
50 rdf:type schema:PropertyValue
51 Nbc545c351c744c2f95face4e16e4cd2b schema:name readcube_id
52 schema:value df28a1767b592cb84afa470e4561d867e9f5a72d60ae25d41707c01f27cf8bcb
53 rdf:type schema:PropertyValue
54 Nc85103ffce2a43ea9f382405f2f805f5 schema:location New York, NY
55 schema:name Springer New York
56 rdf:type schema:Organisation
57 Ncad4b7b671404a3cb209258cadf7361b schema:familyName Jagers
58 schema:givenName Peter
59 rdf:type schema:Person
60 Ne5d6b1b3cb4842c4b2c7a160a770b67d schema:name Springer Nature - SN SciGraph project
61 rdf:type schema:Organization
62 Nf791adc61efe42b1bf1daa6acff86217 rdf:first Ncad4b7b671404a3cb209258cadf7361b
63 rdf:rest rdf:nil
64 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
65 schema:name Engineering
66 rdf:type schema:DefinedTerm
67 anzsrc-for:0904 schema:inDefinedTermSet anzsrc-for:
68 schema:name Chemical Engineering
69 rdf:type schema:DefinedTerm
70 sg:person.011120311545.44 schema:affiliation https://www.grid.ac/institutes/grid.5329.d
71 schema:familyName Drmota
72 schema:givenName Michael
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011120311545.44
74 rdf:type schema:Person
75 sg:person.011756451263.50 schema:affiliation https://www.grid.ac/institutes/grid.426543.2
76 schema:familyName Vatutin
77 schema:givenName Vladimir
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011756451263.50
79 rdf:type schema:Person
80 https://doi.org/10.1006/eujc.1994.1016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035948447
81 rdf:type schema:CreativeWork
82 https://doi.org/10.1016/0097-3165(73)90038-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042257341
83 rdf:type schema:CreativeWork
84 https://doi.org/10.1016/0097-3165(94)90011-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050240691
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1137/0403019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062844610
87 rdf:type schema:CreativeWork
88 https://doi.org/10.1515/dma.1994.4.1.45 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003202694
89 rdf:type schema:CreativeWork
90 https://www.grid.ac/institutes/grid.426543.2 schema:alternateName Steklov Mathematical Institute
91 schema:name Steklov Mathematical Institute, 42 Vavilov Street, 117 966, Moscow, GSP-1, Russia
92 rdf:type schema:Organization
93 https://www.grid.ac/institutes/grid.5329.d schema:alternateName TU Wien
94 schema:name Department of Discrete Mathematics, Technical University of Vienna, Wiedner Hauptstraße 8-10/118, A-1040, Vienna, Austria
95 rdf:type schema:Organization
 




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


...