| Titre : | Stochastic Differential Equations And Stochastic Flows Of Diffeomorphisms |
| Auteurs : | Benziadi Fatima, Directeur de thèse ; Sofiane Ould ouali, Auteur |
| Type de document : | texte imprimé |
| Editeur : | université Dr mouley tahar, Faculté de Science, Saida, Algerie : Alger: univ-saida, 2018 |
| ISBN/ISSN/EAN : | SCT01563 |
| Format : | 47p / 21cm 27cm |
| Langues: | Anglais |
| Mots-clés: | Mathématique ; Stochastic integrals ; Stochastic differential |
| Résumé : |
This research project would not have been possible without the support of many people, therefore i would like to take this opportunity to thank them. First and for most, i would like to thank my supervisor Miss Benziadi Fatima, for the valuable guidance and advice, her assistance and support contributed tremendously in the realization of this humble work. I would also like to extend my special thanks to my respected teachers, with a special mention to the head of laboratory Mr. Kandouci , for their understanding, encouragement and personal attention |
| Note de contenu : |
Introduction 5 1 Stochastic calculus for continuous semi-martingales 7 1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Quadratic variations of continuous semi-martingales . . . . . . . . . . 10 M loc c 1.3 Continuity of quadratic variations in M c and . . . . . . . . . . . 12 1.4 Joint quadratic variations . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Stochastic integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Stochastic integrals of vector valued processes . . . . . . . . . . . . . 18 1.7 Regularity of integrals with respect to parameters . . . . . . . . . . . 20 1.8 Itô’s formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.9 Brownian motion and stochastic intagrals . . . . . . . . . . . . . . . . 26 1.10 Kolmogorov’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2 Stochastic differential equations and stochastic flows of homeomor- phisms 29 2.1 Stochastic differential equation with Lipschitz continuous coefficients 29 2.2 Continuity of the solution with respect to the initial data . . . . . . . 33 2.3 Smoothness of the solution with respect to the initial data . . . . . . 39 2.4 Stochastic flow of homeomorphisms . . . . . . . . . . . . . . . . . . . 45 Conclusion |
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