Approximation schemes for path integration on Riemannian manifolds

Truth is much too complicated to allow anything but approximations. [John von Neumann] In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for L1-functionals, of the approach followed by Andersson and...

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Detalhes bibliográficos
Autor: Sampedro Pascual, Juan Carlos
Tipo de documento: artigo
Data de publicação:2022
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/37978
Acesso em linha:https://hdl.handle.net/10902/37978
Access Level:Acceso aberto
Palavra-chave:Finite dimensional approximations
Riemannian manifolds
Stratonovich stochastic integral
Wiener measure
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spelling Approximation schemes for path integration on Riemannian manifoldsSampedro Pascual, Juan CarlosFinite dimensional approximationsRiemannian manifoldsStratonovich stochastic integralWiener measureTruth is much too complicated to allow anything but approximations. [John von Neumann] In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for L1-functionals, of the approach followed by Andersson and Driver on [1]. We follow a new approach motived by the categorical concept of colimit.The author has been supported by the Research Grant PGC2018-097104-B-I00 of the Spanish Ministry of Science, Technology and Universities, by the Institute of Interdisciplinar Mathematics of Complutense University and by PhD Grant PRE2019_1_0220 of the Basque Country Government.Academic Press Inc.Universidad de Cantabria20222022-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/37978Journal of Mathematical Analysis and Applications, 2022, 512(2), 126176reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/379782026-06-02T12:39:31Z
dc.title.none.fl_str_mv Approximation schemes for path integration on Riemannian manifolds
title Approximation schemes for path integration on Riemannian manifolds
spellingShingle Approximation schemes for path integration on Riemannian manifolds
Sampedro Pascual, Juan Carlos
Finite dimensional approximations
Riemannian manifolds
Stratonovich stochastic integral
Wiener measure
title_short Approximation schemes for path integration on Riemannian manifolds
title_full Approximation schemes for path integration on Riemannian manifolds
title_fullStr Approximation schemes for path integration on Riemannian manifolds
title_full_unstemmed Approximation schemes for path integration on Riemannian manifolds
title_sort Approximation schemes for path integration on Riemannian manifolds
dc.creator.none.fl_str_mv Sampedro Pascual, Juan Carlos
author Sampedro Pascual, Juan Carlos
author_facet Sampedro Pascual, Juan Carlos
author_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Finite dimensional approximations
Riemannian manifolds
Stratonovich stochastic integral
Wiener measure
topic Finite dimensional approximations
Riemannian manifolds
Stratonovich stochastic integral
Wiener measure
description Truth is much too complicated to allow anything but approximations. [John von Neumann] In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for L1-functionals, of the approach followed by Andersson and Driver on [1]. We follow a new approach motived by the categorical concept of colimit.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/37978
url https://hdl.handle.net/10902/37978
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Academic Press Inc.
publisher.none.fl_str_mv Academic Press Inc.
dc.source.none.fl_str_mv Journal of Mathematical Analysis and Applications, 2022, 512(2), 126176
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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