Statistical algorithms for solving the Cauchy problem for second-order parabolic equations: The “dual” scheme View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2012-03

AUTHORS

A. S. Sipin

ABSTRACT

This paper is a continuation of [A. S. Sipin, “Statistical Algorithms for Solving the Cauchy Problem for Second-Order Parabolic Equations,” Vestn. S.-Peterburg. Univ., Mat. Mekh. Astron., No. 3, 65–74 (2011)]. A new algorithm of the Monte Carlo method for solving the Cauchy problem for a second-order parabolic equation with smooth coefficients is considered. Unbiased estimators for functionals of the solutions of this problem are constructed. Unlike in the paper cited above, the “dual” scheme of constructing unbiased estimators for functionals of the solutions of an integral equation equivalent to the Cauchy problem is considered. This simplifies the modeling procedure, because the boundaries of the spectrum for the matrix of the leading coefficients in the equation are not required to be known. More... »

PAGES

35-44

Identifiers

URI

http://scigraph.springernature.com/pub.10.3103/s1063454112010074

DOI

http://dx.doi.org/10.3103/s1063454112010074

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1004039301


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "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": {
          "alternateName": "Vologda State Pedagogical University", 
          "id": "https://www.grid.ac/institutes/grid.445062.1", 
          "name": [
            "Vologda State Pedagogical University, Vologda, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sipin", 
        "givenName": "A. S.", 
        "id": "sg:person.010524252317.52", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010524252317.52"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2012-03", 
    "datePublishedReg": "2012-03-01", 
    "description": "This paper is a continuation of [A. S. Sipin, \u201cStatistical Algorithms for Solving the Cauchy Problem for Second-Order Parabolic Equations,\u201d Vestn. S.-Peterburg. Univ., Mat. Mekh. Astron., No. 3, 65\u201374 (2011)]. A new algorithm of the Monte Carlo method for solving the Cauchy problem for a second-order parabolic equation with smooth coefficients is considered. Unbiased estimators for functionals of the solutions of this problem are constructed. Unlike in the paper cited above, the \u201cdual\u201d scheme of constructing unbiased estimators for functionals of the solutions of an integral equation equivalent to the Cauchy problem is considered. This simplifies the modeling procedure, because the boundaries of the spectrum for the matrix of the leading coefficients in the equation are not required to be known.", 
    "genre": "research_article", 
    "id": "sg:pub.10.3103/s1063454112010074", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136546", 
        "issn": [
          "1025-3106", 
          "1063-4541"
        ], 
        "name": "Vestnik St. Petersburg University, Mathematics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "45"
      }
    ], 
    "name": "Statistical algorithms for solving the Cauchy problem for second-order parabolic equations: The \u201cdual\u201d scheme", 
    "pagination": "35-44", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "133eded3227c7840abe6c0167a9233adb7f9c5bed4a524e2263156e611901221"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.3103/s1063454112010074"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1004039301"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.3103/s1063454112010074", 
      "https://app.dimensions.ai/details/publication/pub.1004039301"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T15:49", 
    "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/v90/0000000001_0000000264/records_8664_00000503.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.3103/S1063454112010074"
  }
]
 

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.10.3103/s1063454112010074'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.3103/s1063454112010074'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.3103/s1063454112010074'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.3103/s1063454112010074'


 

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

61 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.3103/s1063454112010074 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nc0b346d520c2490ab9c6c13fc1bf6db0
4 schema:datePublished 2012-03
5 schema:datePublishedReg 2012-03-01
6 schema:description This paper is a continuation of [A. S. Sipin, “Statistical Algorithms for Solving the Cauchy Problem for Second-Order Parabolic Equations,” Vestn. S.-Peterburg. Univ., Mat. Mekh. Astron., No. 3, 65–74 (2011)]. A new algorithm of the Monte Carlo method for solving the Cauchy problem for a second-order parabolic equation with smooth coefficients is considered. Unbiased estimators for functionals of the solutions of this problem are constructed. Unlike in the paper cited above, the “dual” scheme of constructing unbiased estimators for functionals of the solutions of an integral equation equivalent to the Cauchy problem is considered. This simplifies the modeling procedure, because the boundaries of the spectrum for the matrix of the leading coefficients in the equation are not required to be known.
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N9e3ef52039be4248a4e2cd1722dcec5a
11 Ne50dd9dfe94048ee9866673e13440ff6
12 sg:journal.1136546
13 schema:name Statistical algorithms for solving the Cauchy problem for second-order parabolic equations: The “dual” scheme
14 schema:pagination 35-44
15 schema:productId N0a5edc7f09dc4642ba39d6133d6b89eb
16 N6525965ff6364fb4bb7303bdb2be6281
17 Nd4784fc7e421401483476549c54b1744
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004039301
19 https://doi.org/10.3103/s1063454112010074
20 schema:sdDatePublished 2019-04-10T15:49
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher Na3bfc1b40b304da3af228557d618e16a
23 schema:url http://link.springer.com/10.3103/S1063454112010074
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N0a5edc7f09dc4642ba39d6133d6b89eb schema:name dimensions_id
28 schema:value pub.1004039301
29 rdf:type schema:PropertyValue
30 N6525965ff6364fb4bb7303bdb2be6281 schema:name readcube_id
31 schema:value 133eded3227c7840abe6c0167a9233adb7f9c5bed4a524e2263156e611901221
32 rdf:type schema:PropertyValue
33 N9e3ef52039be4248a4e2cd1722dcec5a schema:issueNumber 1
34 rdf:type schema:PublicationIssue
35 Na3bfc1b40b304da3af228557d618e16a schema:name Springer Nature - SN SciGraph project
36 rdf:type schema:Organization
37 Nc0b346d520c2490ab9c6c13fc1bf6db0 rdf:first sg:person.010524252317.52
38 rdf:rest rdf:nil
39 Nd4784fc7e421401483476549c54b1744 schema:name doi
40 schema:value 10.3103/s1063454112010074
41 rdf:type schema:PropertyValue
42 Ne50dd9dfe94048ee9866673e13440ff6 schema:volumeNumber 45
43 rdf:type schema:PublicationVolume
44 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
45 schema:name Mathematical Sciences
46 rdf:type schema:DefinedTerm
47 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
48 schema:name Pure Mathematics
49 rdf:type schema:DefinedTerm
50 sg:journal.1136546 schema:issn 1025-3106
51 1063-4541
52 schema:name Vestnik St. Petersburg University, Mathematics
53 rdf:type schema:Periodical
54 sg:person.010524252317.52 schema:affiliation https://www.grid.ac/institutes/grid.445062.1
55 schema:familyName Sipin
56 schema:givenName A. S.
57 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010524252317.52
58 rdf:type schema:Person
59 https://www.grid.ac/institutes/grid.445062.1 schema:alternateName Vologda State Pedagogical University
60 schema:name Vologda State Pedagogical University, Vologda, Russia
61 rdf:type schema:Organization
 




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


...