Lifting theorems for some clases of two parameter martingales

By means of nonstandard analysis we establish some lifting theorerms for two parameter stochastic processes, for two parameter martingales and for weak, strong and i-martingales. We also prove that the standard part of an internal martingale is a standard larc martingale (a two parameter version of...

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Autores:
Muñoz de Özak, Myriam
Tipo de recurso:
Article of journal
Fecha de publicación:
1998
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/43684
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/43684
http://bdigital.unal.edu.co/33782/
Palabra clave:
Strong
weak
lare and i-martingales
stochastic processes lifting of a strochastic process and of a martingale
stochastic integration
nonstandard analysis
Brownian motion
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/43684
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network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Muñoz de Özak, Myriam951ebc25-7dc3-4752-9b56-133f0cd9b12b3002019-06-28T12:18:25Z2019-06-28T12:18:25Z1998https://repositorio.unal.edu.co/handle/unal/43684http://bdigital.unal.edu.co/33782/By means of nonstandard analysis we establish some lifting theorerms for two parameter stochastic processes, for two parameter martingales and for weak, strong and i-martingales. We also prove that the standard part of an internal martingale is a standard larc martingale (a two parameter version of a cadlag martingale). A basic nonstandard two parameter stochastic integral is introduced. An integral representation of Wong and Zakai proves to be a very useful tool for our purposes.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33685Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 32, núm. 1 (1998); 45-71 0034-7426Muñoz de Özak, Myriam (1998) Lifting theorems for some clases of two parameter martingales. Revista Colombiana de Matemáticas; Vol. 32, núm. 1 (1998); 45-71 0034-7426 .Lifting theorems for some clases of two parameter martingalesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTStrongweaklare and i-martingalesstochastic processes lifting of a strochastic process and of a martingalestochastic integrationnonstandard analysisBrownian motionORIGINAL33685-125602-1-PB.pdfapplication/pdf12830284https://repositorio.unal.edu.co/bitstream/unal/43684/1/33685-125602-1-PB.pdf678fd78d7fe9fa9da31d25fd790cd52cMD51THUMBNAIL33685-125602-1-PB.pdf.jpg33685-125602-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6842https://repositorio.unal.edu.co/bitstream/unal/43684/2/33685-125602-1-PB.pdf.jpg7b80d956345ef3af6ab3dabc75728e5aMD52unal/43684oai:repositorio.unal.edu.co:unal/436842024-02-11 23:18:53.741Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Lifting theorems for some clases of two parameter martingales
title Lifting theorems for some clases of two parameter martingales
spellingShingle Lifting theorems for some clases of two parameter martingales
Strong
weak
lare and i-martingales
stochastic processes lifting of a strochastic process and of a martingale
stochastic integration
nonstandard analysis
Brownian motion
title_short Lifting theorems for some clases of two parameter martingales
title_full Lifting theorems for some clases of two parameter martingales
title_fullStr Lifting theorems for some clases of two parameter martingales
title_full_unstemmed Lifting theorems for some clases of two parameter martingales
title_sort Lifting theorems for some clases of two parameter martingales
dc.creator.fl_str_mv Muñoz de Özak, Myriam
dc.contributor.author.spa.fl_str_mv Muñoz de Özak, Myriam
dc.subject.proposal.spa.fl_str_mv Strong
weak
lare and i-martingales
stochastic processes lifting of a strochastic process and of a martingale
stochastic integration
nonstandard analysis
Brownian motion
topic Strong
weak
lare and i-martingales
stochastic processes lifting of a strochastic process and of a martingale
stochastic integration
nonstandard analysis
Brownian motion
description By means of nonstandard analysis we establish some lifting theorerms for two parameter stochastic processes, for two parameter martingales and for weak, strong and i-martingales. We also prove that the standard part of an internal martingale is a standard larc martingale (a two parameter version of a cadlag martingale). A basic nonstandard two parameter stochastic integral is introduced. An integral representation of Wong and Zakai proves to be a very useful tool for our purposes.
publishDate 1998
dc.date.issued.spa.fl_str_mv 1998
dc.date.accessioned.spa.fl_str_mv 2019-06-28T12:18:25Z
dc.date.available.spa.fl_str_mv 2019-06-28T12:18:25Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.coarversion.spa.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
format http://purl.org/coar/resource_type/c_6501
status_str publishedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/43684
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/33782/
url https://repositorio.unal.edu.co/handle/unal/43684
http://bdigital.unal.edu.co/33782/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/33685
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 32, núm. 1 (1998); 45-71 0034-7426
dc.relation.references.spa.fl_str_mv Muñoz de Özak, Myriam (1998) Lifting theorems for some clases of two parameter martingales. Revista Colombiana de Matemáticas; Vol. 32, núm. 1 (1998); 45-71 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/43684/1/33685-125602-1-PB.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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