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Brownian motion, martingales, and stochastic calculus / Jean-François Le Gall (2016)  

Public Titre : Brownian motion, martingales, and stochastic calculus Type de document : Guide/Manuel Auteurs : Jean-François Le Gall, Auteur Editeur : Springer International Publishing Année de publication : 2016 Importance : 273 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-319-31089-3 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] chaîne de Markov [Termes IGN] fonction harmonique [Termes IGN] mouvement brownien [Termes IGN] probabilités [Termes IGN] stochastique Résumé : (éditeur) 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 stepping 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. Numéro de notice : 26586 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel En ligne : https://doi.org/10.1007/978-3-319-31089-3 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95220