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Titre : | On the study of some class of self-similar stochastic processes |
Auteurs : | Idrissi Soumia, Directeur de thèse ; Aimane Mammeri, Auteur |
Type de document : | texte imprimé |
Editeur : | université Dr mouley tahar, Faculté des Sciences, Saida, Algerie : Alger: univ-saida, 2018 |
ISBN/ISSN/EAN : | SCT01534 |
Format : | 75p / 21cm27cm |
Langues: | Anglais |
Catégories : | |
Mots-clés: | Self-similar processes ; Brownian motion ; Fractional Brownain motion ; Fractional derivatives and integrals ; Mittag-Leffler function ; Grey noise ; Grey Brownian motion. |
Résumé : |
this work provides an important step in the construction, definition and the study of
a class of H-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that evolves in time according to a differential equation of fractional type. This construction is based on the theory of finite measures on functional spaces. First, we brought the reader through the fundamental notions of stochastic processes and stochastic integration as well. In particular, within the study of H−sssi processes. Then, we focused on fractional Brownian motion (fBm), and introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. We introduced and stud- ied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H−sssi processes. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the un- derline probability space. We also pointed out that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. |
Note de contenu : |
Introduction
1 Background on stochastic calculus 2 Fractional Brownian motion 3 Introduction to Fractional calculus 4 Grey Brawnian motion Conclusion |
Exemplaires (1)
Code-barres | Cote | Support | Localisation | Section | Disponibilité |
---|---|---|---|---|---|
SCT01534 | TMMS00334 | Périodique | Salle des Thèses | Mathématique | Exclu du prêt |
Documents numériques (1)
On the study of some class of self-similar stochastic processes Adobe Acrobat PDF |