Author: J. Jacod
Publisher: Springer
ISBN: 3540353011
Category : Mathematics
Languages : fr
Pages : 550

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Author: Jean-François Le Gall
Publisher: Springer
ISBN: 3319310895
Category : Mathematics
Languages : en
Pages : 282

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Book Description
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Author:
Publisher: Ed. Techniques Ingénieur
ISBN:
Category :
Languages : fr
Pages : 24

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Author: Daniel Revuz
Publisher: Springer Science & Business Media
ISBN: 3662217260
Category : Mathematics
Languages : en
Pages : 544

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Book Description
This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).

Author: Daniel Revuz
Publisher: Springer Science & Business Media
ISBN: 3662064006
Category : Mathematics
Languages : en
Pages : 608

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Book Description
"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.

Author: Léonard Gallardo
Publisher: Editions Hermann
ISBN: 9782705667979
Category :
Languages : fr
Pages : 239

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Book Description
Le mouvement brownien est l'objet central du calcul des probabilités modernes : il est à la fois une martingale, un processus gaussien, un processus à accroissements indépendants et un processus de Markov. Présentation de ses propriétés avec les deux outils qu'il permet de développer : l'intégrale d'Itô et la notion d'équation différentielle stochastique. Avec des exercices de difficulté variée.

Author: Jacques Azema
Publisher: Séminaire de Probabilités
ISBN:
Category : Mathematics
Languages : en
Pages : 664

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Author: Sabin Lessard
Publisher: Editions Ellipses
ISBN: 2340083230
Category : Mathematics
Languages : fr
Pages : 287

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Book Description
Dans cet ouvrage, on traite principalement de chaînes de Markov qui servent à modéliser les changements d'état aléatoires au cours du temps. Il y est aussi question de processus de renouvellement, de martingales et du mouvement brownien. On propose des nombreux exemples, en biologie avec des modèles de reproduction de populations, en finance avec le cours d'un actif, ou encore en recherche opérationnelle avec des files d'attente et des modèles de fiabilité. Les principaux résultats théoriques sont démontrés à la fin des chapitres pour les plus exigeants. Dans sa deuxième édition, l'ouvrage comporte 121 exercices et leurs corrigés détaillés. Cet ouvrage est à destination des étudiants et de licence en maths, en génie et en sciences naturelles, économiques ou de gestion, qui veulent approfondir la théorie des probabilités.

Author: Nicolas Savy
Publisher:
ISBN:
Category :
Languages : fr
Pages : 198

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Book Description
Le mouvement Brownien fractionnaire (mBf) est devenu un processus incontournable dès que l'on veut s'affranchir des propriétés de Markov et d'indépendance des accroissements. Nous verrons les principales propriétés de ce processus, nous insisterons sur certains aspects de son utilisation comme modèle de file fluide. On développe ensuite la construction d'une intégrale anticipative relative au mBf à partir de l'intégrale anticipative relative au mouvement Brownien. Fort de cette idée, nous avons introduit une intégrale anticipative relative à des processus de Poissons filtrés (pPf) à partir d'une intégrale anticipative pour des processus de Poissons marqués, intégrale que nous relions à l'intégrale de Stieltjès. L'étude se poursuit par une formule de Itô pour des fonctionnelles cylindriques et par un résultat sur la continuité de Holdër des processus intégrés. Pour finir, un théorème de convergence en loi d'une suite de pPf vers un processus de Volterra est établi.

Author: D. Revuz
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 560

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Book Description
This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).