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Probabilités et potentiel, Volume 5: Processus de Markov, compléments aux calculs stochastiques
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ISBN10: 2705614346
ISBN13: 9782705614348
Publisher: Hermann
Published: Feb 22 2008
Pages: 450
Weight: 1.66
Height: 0.91 Width: 6.63 Depth: 10.25
Language: French
ISBN13: 9782705614348
Publisher: Hermann
Published: Feb 22 2008
Pages: 450
Weight: 1.66
Height: 0.91 Width: 6.63 Depth: 10.25
Language: French
Ce traité en 5 tomes, qui expose les relations entre la théorie du potentiel et celle des processus stochastiques, s'adresse à tous les ingénieurs ou scientifiques utilisant les probabilités. Sommaire: I. Espaces Mesurables, Chapitres 1 à 4 Lois de probabilité et espérances mathématiques; compléments de théorie de la mesure; processus stochastiques. II. Théorie des martingales, Chapitres 5 à 8 Généralités et cas discret; Martingales en temps continu; Décomposition des surmartingales applications; Intégrales stochastiques structure des martingales. III. Théorie discrète du potentiel, Chapitres 9 à 11 Noyaux et fonctions excessives. théorie des réduites et du balayage. Méthodes nouvelles en théorie des capacités, application aux maisons de jeux. IV. Théorie du potentiel associée à une résolvante, Chapitres 12 à 16 Semi-groupes et résolvantes; Construction de résolvantes et de semi-groupes; Processusde Markov; Fonctions excessives et fonctionnelles additives: processus droits et transformations multiplicatives; V. Processus de Markov: compléments aux calculs stochastiques, Chapitres 17 à 24 rappels sur les processus droits, processus homogènes, retournement du temps; Processus à naissance aléatoire; Ensembles aléatoires, excursions; Décompositions chaotiques, . Quelques applications à l'analyse. Compléments de calcul stochastique. Récurence transfinie et mesurabilité.
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