Iterated logarithm law for anticipating stochastic differential equations

We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations $$ \xi_t^u=X_0^u+\frac{1}{\sqrt{\log \log u}} \sum_{j=1}^k \int_0^t A_j^u\left(\xi_s^u\right) \circ d W_s^j+\int_0^t A_0^u\left(\xi_s^u\right) d s $$ where $u>e, W=\left\{\left...

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Detalles Bibliográficos
Autores: Márquez, David (Márquez Carreras), Rovira Escofet, Carles
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2007
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/216550
Acceso en línea:https://hdl.handle.net/2445/216550
Access Level:acceso abierto
Palabra clave:Equacions diferencials estocàstiques
Anàlisi estocàstica
Stochastic differential equations
Stochastic analysis
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spelling Iterated logarithm law for anticipating stochastic differential equationsMárquez, David (Márquez Carreras)Rovira Escofet, CarlesEquacions diferencials estocàstiquesAnàlisi estocàsticaStochastic differential equationsStochastic analysisWe prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations $$ \xi_t^u=X_0^u+\frac{1}{\sqrt{\log \log u}} \sum_{j=1}^k \int_0^t A_j^u\left(\xi_s^u\right) \circ d W_s^j+\int_0^t A_0^u\left(\xi_s^u\right) d s $$ where $u>e, W=\left\{\left(W_t^1, \ldots, W_t^k\right), 0 \leq t \leq 1\right\}$ is a standard $k$ dimensional Wiener process, $A_0^u, A_1^u, \ldots, A_k^u: \mathbb{R}^d \longrightarrow \mathbb{R}^d$ are functions of class $\mathcal{C}^2$ with bounded partial derivatives up to order $2, X_0^u$ is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral .Springer Verlag2024202420072024info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion14 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/216550Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1007/s10959-007-0114-xJournal of Theoretical Probability, 2007, vol. 21, num.3, p. 650-659https://doi.org/10.1007/s10959-007-0114-x(c) Springer Verlag, 2007info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2165502026-05-29T05:05:01Z
dc.title.none.fl_str_mv Iterated logarithm law for anticipating stochastic differential equations
title Iterated logarithm law for anticipating stochastic differential equations
spellingShingle Iterated logarithm law for anticipating stochastic differential equations
Márquez, David (Márquez Carreras)
Equacions diferencials estocàstiques
Anàlisi estocàstica
Stochastic differential equations
Stochastic analysis
title_short Iterated logarithm law for anticipating stochastic differential equations
title_full Iterated logarithm law for anticipating stochastic differential equations
title_fullStr Iterated logarithm law for anticipating stochastic differential equations
title_full_unstemmed Iterated logarithm law for anticipating stochastic differential equations
title_sort Iterated logarithm law for anticipating stochastic differential equations
dc.creator.none.fl_str_mv Márquez, David (Márquez Carreras)
Rovira Escofet, Carles
author Márquez, David (Márquez Carreras)
author_facet Márquez, David (Márquez Carreras)
Rovira Escofet, Carles
author_role author
author2 Rovira Escofet, Carles
author2_role author
dc.subject.none.fl_str_mv Equacions diferencials estocàstiques
Anàlisi estocàstica
Stochastic differential equations
Stochastic analysis
topic Equacions diferencials estocàstiques
Anàlisi estocàstica
Stochastic differential equations
Stochastic analysis
description We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations $$ \xi_t^u=X_0^u+\frac{1}{\sqrt{\log \log u}} \sum_{j=1}^k \int_0^t A_j^u\left(\xi_s^u\right) \circ d W_s^j+\int_0^t A_0^u\left(\xi_s^u\right) d s $$ where $u>e, W=\left\{\left(W_t^1, \ldots, W_t^k\right), 0 \leq t \leq 1\right\}$ is a standard $k$ dimensional Wiener process, $A_0^u, A_1^u, \ldots, A_k^u: \mathbb{R}^d \longrightarrow \mathbb{R}^d$ are functions of class $\mathcal{C}^2$ with bounded partial derivatives up to order $2, X_0^u$ is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral .
publishDate 2007
dc.date.none.fl_str_mv 2007
2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/216550
url https://hdl.handle.net/2445/216550
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1007/s10959-007-0114-x
Journal of Theoretical Probability, 2007, vol. 21, num.3, p. 650-659
https://doi.org/10.1007/s10959-007-0114-x
dc.rights.none.fl_str_mv (c) Springer Verlag, 2007
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Verlag, 2007
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 14 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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