Ontology type: schema:ScholarlyArticle Open Access: True
2009-11
AUTHORSLuigi Ambrosio, Giuseppe Savaré, Lorenzo Zambotti
ABSTRACTWe study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition probabilities. The main result is the following stability property: if the associated invariant measures converge weakly, then the Markov processes converge in law. The proofs are based on the interpretation of a Fokker–Planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures, endowed with the Wasserstein distance. More... »
PAGES517-564
http://scigraph.springernature.com/pub.10.1007/s00440-008-0177-3
DOIhttp://dx.doi.org/10.1007/s00440-008-0177-3
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1009102645
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/2008/0102",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Applied 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": "Scuola Normale Superiore di Pisa",
"id": "https://www.grid.ac/institutes/grid.6093.c",
"name": [
"Scuola Normale Superiore, Pisa, Italy"
],
"type": "Organization"
},
"familyName": "Ambrosio",
"givenName": "Luigi",
"id": "sg:person.012621721115.68",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Pavia",
"id": "https://www.grid.ac/institutes/grid.8982.b",
"name": [
"Dipartimento di Matematica, Universit\u00e0 di Pavia, Pavia, Italy"
],
"type": "Organization"
},
"familyName": "Savar\u00e9",
"givenName": "Giuseppe",
"id": "sg:person.015505046621.07",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015505046621.07"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires",
"id": "https://www.grid.ac/institutes/grid.463951.c",
"name": [
"Universit\u00e9 Pierre et Marie Curie, LPMA, 4 place Jussieu, 75252, Paris cedex 05, France"
],
"type": "Organization"
},
"familyName": "Zambotti",
"givenName": "Lorenzo",
"id": "sg:person.016653055203.64",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016653055203.64"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/s002200050080",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000138621",
"https://doi.org/10.1007/s002200050080"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1000664213",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-77739-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000664213",
"https://doi.org/10.1007/978-3-642-77739-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-77739-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000664213",
"https://doi.org/10.1007/978-3-642-77739-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02018814",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003362939",
"https://doi.org/10.1007/bf02018814"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02018814",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003362939",
"https://doi.org/10.1007/bf02018814"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01049962",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1010097434",
"https://doi.org/10.1007/bf01049962"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-540-34514-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012306418",
"https://doi.org/10.1007/978-3-540-34514-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-540-34514-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012306418",
"https://doi.org/10.1007/978-3-540-34514-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00440-003-0307-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1016184078",
"https://doi.org/10.1007/s00440-003-0307-x"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00440-003-0307-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1016184078",
"https://doi.org/10.1007/s00440-003-0307-x"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0304-4149(00)00104-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019284837"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s004400200214",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022357646",
"https://doi.org/10.1007/s004400200214"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s004400200214",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022357646",
"https://doi.org/10.1007/s004400200214"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01195389",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023229269",
"https://doi.org/10.1007/bf01195389"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01195389",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023229269",
"https://doi.org/10.1007/bf01195389"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1023634439",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-662-21726-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023634439",
"https://doi.org/10.1007/978-3-662-21726-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-662-21726-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023634439",
"https://doi.org/10.1007/978-3-662-21726-9"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1515/form.2005.17.3.343",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024589590"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/aima.1997.1634",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025395081"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1026608331",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3-540-28999-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026608331",
"https://doi.org/10.1007/3-540-28999-2"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3-540-28999-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026608331",
"https://doi.org/10.1007/3-540-28999-2"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160370408",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026620351"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160370408",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026620351"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00440-004-0335-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1033646368",
"https://doi.org/10.1007/s00440-004-0335-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00440-004-0335-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1033646368",
"https://doi.org/10.1007/s00440-004-0335-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s004400200203",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036633560",
"https://doi.org/10.1007/s004400200203"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s004400200203",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036633560",
"https://doi.org/10.1007/s004400200203"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00028-006-0275-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038258298",
"https://doi.org/10.1007/s00028-006-0275-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-005-0386-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044755766",
"https://doi.org/10.1007/s00205-005-0386-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-005-0386-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044755766",
"https://doi.org/10.1007/s00205-005-0386-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02384761",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045346613",
"https://doi.org/10.1007/bf02384761"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02384761",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045346613",
"https://doi.org/10.1007/bf02384761"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02304888",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1050743391",
"https://doi.org/10.1007/bf02304888"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02304888",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1050743391",
"https://doi.org/10.1007/bf02304888"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/1106035",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062864358"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/s0036141096303359",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062876406"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/009117906000000773",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064389381"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/ejp.v13-525",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064396609"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/aop/1015345767",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064402853"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/aop/1022855642",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064403050"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/aop/1046294313",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064403325"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1515/9783110889741",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1096915525"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/cbo9780511662829",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1098701315"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/gsm/058",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1098710084"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/surv/062",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1098741760"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.32917/hmj/1206135203",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1110317763"
],
"type": "CreativeWork"
}
],
"datePublished": "2009-11",
"datePublishedReg": "2009-11-01",
"description": "We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition probabilities. The main result is the following stability property: if the associated invariant measures converge weakly, then the Markov processes converge in law. The proofs are based on the interpretation of a Fokker\u2013Planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures, endowed with the Wasserstein distance.",
"genre": "research_article",
"id": "sg:pub.10.1007/s00440-008-0177-3",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isPartOf": [
{
"id": "sg:journal.1053886",
"issn": [
"0178-8051",
"1432-2064"
],
"name": "Probability Theory and Related Fields",
"type": "Periodical"
},
{
"issueNumber": "3-4",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "145"
}
],
"name": "Existence and stability for Fokker\u2013Planck equations with log-concave reference measure",
"pagination": "517-564",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"2b5dca6a68d5110bddf599169f3e2252e233f847ddb9fbbcca8ac229cce7c734"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s00440-008-0177-3"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1009102645"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s00440-008-0177-3",
"https://app.dimensions.ai/details/publication/pub.1009102645"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-11T14:28",
"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/v90/0000000373_0000000373/records_13084_00000000.jsonl",
"type": "ScholarlyArticle",
"url": "https://link.springer.com/10.1007%2Fs00440-008-0177-3"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
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/s00440-008-0177-3'
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/s00440-008-0177-3'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00440-008-0177-3'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00440-008-0177-3'
This table displays all metadata directly associated to this object as RDF triples.
199 TRIPLES
21 PREDICATES
62 URIs
19 LITERALS
7 BLANK NODES