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Backward stochastic differential equations driven by Gaussian Volterra processes

Author: Habiba KnaniMarco DozziKhalifa El MabroukIvan NourdinRafik AguechAll authors
Publisher: 2020.
Dissertation: Thèse de doctorat : Mathématiques : Université de Lorraine : 2020.
Thèse de doctorat : Mathématiques : Université du Centre (Sousse, Tunisie) : 2020.
Edition/Format:   Computer file : Document : Thesis/dissertation : English
Summary:
Cette thèse porte sur les équations différentielles stochastiques rétrogrades (EDSR) dirigées par une classe de processus de Volterra qui contient le mouvement brownien multifractionnaire et le processus Ornstein-Uhlenbeck multifractionnaire. Dans la première partie, nous étudions la solution des EDSRs multidimensionnelles avec des générateurs linéaires. Par la formule d'Itô pour les processus de Volterra
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Genre/Form: Thèses et écrits académiques
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Habiba Knani; Marco Dozzi; Khalifa El Mabrouk; Ivan Nourdin; Rafik Aguech; Marie-Claire Quenez; Marianne Clausel; Moez Khenissi; Université de Lorraine.; Université du Centre (Sousse, Tunisie).; École doctorale IAEM Lorraine - Informatique, Automatique, Électronique - Électrotechnique, Mathématiques de Lorraine.; Institut Élie Cartan de Lorraine (2013-.... / Vandoeuvre-lès-Nancy, Metz).
OCLC Number: 1156318686
Notes: Thèse soutenue en co-tutelle.
Titre provenant de l'écran-titre.
Description: 1 online resource
Responsibility: Habiba Knani ; sous la direction de Marco Dozzi et de Khalifa El Mabrouk.

Abstract:

Cette thèse porte sur les équations différentielles stochastiques rétrogrades (EDSR) dirigées par une classe de processus de Volterra qui contient le mouvement brownien multifractionnaire et le processus Ornstein-Uhlenbeck multifractionnaire. Dans la première partie, nous étudions la solution des EDSRs multidimensionnelles avec des générateurs linéaires. Par la formule d'Itô pour les processus de Volterra nous réduisons l'EDSR à une équation aux dérivées partielles (EDP) de second ordre linéaire avec la condition terminale. Sous une condition d'intégrabilité dans un voisinage du temps terminal de la variance du processus de Volterra, nous résolvons l'EDP associée explicitement et en déduisons la solution des EDSR linéaire. Puis, nous discutons une application dans le contexte des stratégies autofinancées. La seconde partie de la thèse traite des EDSRs non linéaires dirigées par la même classe de processus de Volterra. Les résultats principaux sont l'existence et l'unicité de la solution de l'EDSR dans un espace de fonctionnelles régulières du processus de Volterra et un théorème de comparaison qui porte sur les générateurs et les conditions terminales. Nous donnons deux preuves de l'existence et de l'unicité de la solution de l'EDSR, l'une basée sur l'EDP associée et l'autre sans référence à l'EDP, mais avec des méthodes probabilistes. Cette seconde preuve est techniquement difficile et, en raison de l'absence de propriétés de martingale dans le contexte des processus de Volterra, la preuve nécessite différentes normes sur l'espace de Hilbert sous-jacent défini par le noyau du processus de Volterra. Pour la construction de la solution, nous avons besoin de la notion de l'espérance quasi-conditionnelle, d'une formule de type Clark-Ocone et d'une autre formule d'Itô pour les processus de Volterra. Contrairement au cas classique des EDSR dirigées par le mouvement brownien ou brownien fractionnaire, une hypothèse sur le comportement du noyau est nécessaire pour l'existence et l'unicité de la solution de l'EDSR. Pour le mouvement brownien multifractionnaire, cette hypothèse est liée à la fonction de Hurst.

This thesis treats of backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Itoˆ formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. We discuss an application in the context of self-financing trading stategies. The second part of the thesis treats of non-linear BSDE driven by the same class of Gaussian Volterra processes. The main results are the existence and uniqueness of the solution in a space of regular functionals of the Volterra process, and a comparison theorem for the solutions of BSDE. We give two proofs for the existence and uniqueness of the solution, one is based on the associated PDE and a second one without making reference to this PDE, but with probabilistic and functional theoretic methods. Especially this second proof is technically quite complex, and, due to the absence of mar- tingale properties in the context of Volterra processes, requires to work with different norms on the underlying Hilbert space that is defined by the kernel of the Volterra process. For the construction of the solution we need the notion of quasi-conditional expectation, a Clark-Ocone type formula and another Itoˆ formula for Volterra processes. Contrary to the more classical cases of BSDE driven by Brownian or fractional Brownian motion, an assumption on the behaviour of the kernel of the driv- ing Volterra process is in general necessary for the wellposedness of the BSDE. For multifractional Brownian motion this assumption is closely related to the behaviour of the Hurst function.

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# Expression de chaos<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/processus_de_volterra_gaussien<\/a>> ; # Processus de Volterra Gaussien<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/formule_de_clark_ocone<\/a>> ; # Formule de Clark-Ocone<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/equation_aux_derivees_partielles_avec_condition_terminale<\/a>> ; # \u00C9quation aux d\u00E9riv\u00E9es partielles avec condition terminale<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/esperance_quasi_conditionnelle<\/a>> ; # Esp\u00E9rance quasi-conditionnelle<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/volterra_equations_de<\/a>> ; # Volterra, \u00C9quations de<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/515.35\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/mathematiques_financieres<\/a>> ; # Math\u00E9matiques financi\u00E8res<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/formule_de_feynman_kac<\/a>> ; # Formule de Feynman-Kac<\/span>\n\u00A0\u00A0\u00A0\nschema:author<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/knani_habiba_1989<\/a>> ; # Habiba Knani<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/aguech_rafik_19<\/a>> ; # Rafik Aguech<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Organization\/universite_du_centre_sousse_tunisie<\/a>> ; # Universit\u00E9 du Centre (Sousse, Tunisie).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Organization\/ecole_doctorale_iaem_lorraine_informatique_automatique_electronique_electrotechnique_mathematiques_de_lorraine<\/a>> ; # \u00C9cole doctorale IAEM Lorraine - Informatique, Automatique, \u00C9lectronique - \u00C9lectrotechnique, Math\u00E9matiques de Lorraine.<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/clausel_marianne_1974<\/a>> ; # Marianne Clausel<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/nourdin_ivan<\/a>> ; # Ivan Nourdin<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/quenez_marie_claire<\/a>> ; # Marie-Claire Quenez<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Organization\/universite_de_lorraine<\/a>> ; # Universit\u00E9 de Lorraine.<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/dozzi_marco<\/a>> ; # Marco Dozzi<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/khenissi_moez<\/a>> ; # Moez Khenissi<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/el_mabrouk_khalifa<\/a>> ; # Khalifa El Mabrouk<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Organization\/institut_elie_cartan_de_lorraine_2013_vandoeuvre_les_nancy_metz<\/a>> ; # Institut \u00C9lie Cartan de Lorraine (2013-.... \/ Vandoeuvre-l\u00E8s-Nancy, Metz).<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2020<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This thesis treats of backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Ito\u02C6 formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. We discuss an application in the context of self-financing trading stategies. The second part of the thesis treats of non-linear BSDE driven by the same class of Gaussian Volterra processes. The main results are the existence and uniqueness of the solution in a space of regular functionals of the Volterra process, and a comparison theorem for the solutions of BSDE. We give two proofs for the existence and uniqueness of the solution, one is based on the associated PDE and a second one without making reference to this PDE, but with probabilistic and functional theoretic methods. Especially this second proof is technically quite complex, and, due to the absence of mar- tingale properties in the context of Volterra processes, requires to work with different norms on the underlying Hilbert space that is defined by the kernel of the Volterra process. For the construction of the solution we need the notion of quasi-conditional expectation, a Clark-Ocone type formula and another Ito\u02C6 formula for Volterra processes. Contrary to the more classical cases of BSDE driven by Brownian or fractional Brownian motion, an assumption on the behaviour of the kernel of the driv- ing Volterra process is in general necessary for the wellposedness of the BSDE. For multifractional Brownian motion this assumption is closely related to the behaviour of the Hurst function.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Cette th\u00E8se porte sur les \u00E9quations diff\u00E9rentielles stochastiques r\u00E9trogrades (EDSR) dirig\u00E9es par une classe de processus de Volterra qui contient le mouvement brownien multifractionnaire et le processus Ornstein-Uhlenbeck multifractionnaire. Dans la premi\u00E8re partie, nous \u00E9tudions la solution des EDSRs multidimensionnelles avec des g\u00E9n\u00E9rateurs lin\u00E9aires. Par la formule d\'It\u00F4 pour les processus de Volterra nous r\u00E9duisons l\'EDSR \u00E0 une \u00E9quation aux d\u00E9riv\u00E9es partielles (EDP) de second ordre lin\u00E9aire avec la condition terminale. Sous une condition d\'int\u00E9grabilit\u00E9 dans un voisinage du temps terminal de la variance du processus de Volterra, nous r\u00E9solvons l\'EDP associ\u00E9e explicitement et en d\u00E9duisons la solution des EDSR lin\u00E9aire. Puis, nous discutons une application dans le contexte des strat\u00E9gies autofinanc\u00E9es. La seconde partie de la th\u00E8se traite des EDSRs non lin\u00E9aires dirig\u00E9es par la m\u00EAme classe de processus de Volterra. Les r\u00E9sultats principaux sont l\'existence et l\'unicit\u00E9 de la solution de l\'EDSR dans un espace de fonctionnelles r\u00E9guli\u00E8res du processus de Volterra et un th\u00E9or\u00E8me de comparaison qui porte sur les g\u00E9n\u00E9rateurs et les conditions terminales. Nous donnons deux preuves de l\'existence et de l\'unicit\u00E9 de la solution de l\'EDSR, l\'une bas\u00E9e sur l\'EDP associ\u00E9e et l\'autre sans r\u00E9f\u00E9rence \u00E0 l\'EDP, mais avec des m\u00E9thodes probabilistes. Cette seconde preuve est techniquement difficile et, en raison de l\'absence de propri\u00E9t\u00E9s de martingale dans le contexte des processus de Volterra, la preuve n\u00E9cessite diff\u00E9rentes normes sur l\'espace de Hilbert sous-jacent d\u00E9fini par le noyau du processus de Volterra. Pour la construction de la solution, nous avons besoin de la notion de l\'esp\u00E9rance quasi-conditionnelle, d\'une formule de type Clark-Ocone et d\'une autre formule d\'It\u00F4 pour les processus de Volterra. Contrairement au cas classique des EDSR dirig\u00E9es par le mouvement brownien ou brownien fractionnaire, une hypoth\u00E8se sur le comportement du noyau est n\u00E9cessaire pour l\'existence et l\'unicit\u00E9 de la solution de l\'EDSR. Pour le mouvement brownien multifractionnaire, cette hypoth\u00E8se est li\u00E9e \u00E0 la fonction de Hurst.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/10243790598<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Th\u00E8ses et \u00E9crits acad\u00E9miques<\/span>\" ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Backward stochastic differential equations driven by Gaussian Volterra processes<\/span>\" ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"1156318686<\/span>\" ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/docnum.univ-lorraine.fr\/public\/DDOC_T_2020_0014_KNANI.pdf<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.theses.fr\/2020LORR0014\/document<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/1156318686<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/aguech_rafik_19<\/a>> # Rafik Aguech<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"19..<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Aguech<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Rafik<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Rafik Aguech<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/clausel_marianne_1974<\/a>> # Marianne Clausel<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1974<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Clausel<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Marianne<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Marianne Clausel<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/dozzi_marco<\/a>> # Marco Dozzi<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Dozzi<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Marco<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Marco Dozzi<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/el_mabrouk_khalifa<\/a>> # Khalifa El Mabrouk<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"El Mabrouk<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Khalifa<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Khalifa El Mabrouk<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/khenissi_moez<\/a>> # Moez Khenissi<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Khenissi<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Moez<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Moez Khenissi<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/knani_habiba_1989<\/a>> # Habiba Knani<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1989<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Knani<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Habiba<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Habiba Knani<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/nourdin_ivan<\/a>> # Ivan Nourdin<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Nourdin<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Ivan<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Ivan Nourdin<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Person\/quenez_marie_claire<\/a>> # Marie-Claire Quenez<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Quenez<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Marie-Claire<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Marie-Claire Quenez<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/calcul_de_malliavin<\/a>> # Calcul de Malliavin<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Calcul de Malliavin<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/equation_aux_derivees_partielles_avec_condition_terminale<\/a>> # \u00C9quation aux d\u00E9riv\u00E9es partielles avec condition terminale<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9quation aux d\u00E9riv\u00E9es partielles avec condition terminale<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/esperance_quasi_conditionnelle<\/a>> # Esp\u00E9rance quasi-conditionnelle<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Esp\u00E9rance quasi-conditionnelle<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/expression_de_chaos<\/a>> # Expression de chaos<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Expression de chaos<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/formule_de_clark_ocone<\/a>> # Formule de Clark-Ocone<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Formule de Clark-Ocone<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/formule_de_feynman_kac<\/a>> # Formule de Feynman-Kac<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Formule de Feynman-Kac<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/integrale_de_divergence<\/a>> # Int\u00E9grale de divergence<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Int\u00E9grale de divergence<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Thing\/processus_de_volterra_gaussien<\/a>> # Processus de Volterra Gaussien<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Processus de Volterra Gaussien<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/equations_differentielles_stochastiques<\/a>> # \u00C9quations diff\u00E9rentielles stochastiques<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9quations diff\u00E9rentielles stochastiques<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/equations_differentielles_stochastiques_retrogrades<\/a>> # \u00C9quations diff\u00E9rentielles stochastiques r\u00E9trogrades<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"\u00C9quations diff\u00E9rentielles stochastiques r\u00E9trogrades<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/ito_integrales_d<\/a>> # It\u00F4, Int\u00E9grales d\'<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"It\u00F4, Int\u00E9grales d\'<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/mathematiques_financieres<\/a>> # Math\u00E9matiques financi\u00E8res<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Math\u00E9matiques financi\u00E8res<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/processus_gaussiens<\/a>> # Processus gaussiens<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Processus gaussiens<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/10243790598#Topic\/volterra_equations_de<\/a>> # Volterra, \u00C9quations de<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Volterra, \u00C9quations de<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.theses.fr\/2020LORR0014\/document<\/a>>\u00A0\u00A0\u00A0\nrdfs:comment<\/a> \"Acc\u00E8s au texte int\u00E9gral<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/1156318686<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/1156318686<\/a>> ; # Backward stochastic differential equations driven by Gaussian Volterra processes<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2020-10-08<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n