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Brownian Motion, Martingales, and Stochastic Calculus / / by Jean-François Le Gall



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Autore: Le Gall Jean-François Visualizza persona
Titolo: Brownian Motion, Martingales, and Stochastic Calculus / / by Jean-François Le Gall Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Edizione: 1st ed. 2016.
Descrizione fisica: 1 online resource (XIII, 273 p. 5 illus., 1 illus. in color.)
Disciplina: 519.23
Soggetto topico: Probabilities
Social sciences - Mathematics
Measure theory
Mathematical models
System theory
Control theory
Probability Theory
Mathematics in Business, Economics and Finance
Measure and Integration
Mathematical Modeling and Industrial Mathematics
Systems Theory, Control
Note generali: Includes Index.
Nota di contenuto: Gaussian variables and Gaussian processes -- Brownian motion -- Filtrations and martingales -- Continuous semimartingales -- Stochastic integration -- General theory of Markov processes -- Brownian motion and partial differential equations -- Stochastic differential equations -- Local times -- The monotone class lemma -- Discrete martingales -- References.
Sommario/riassunto: 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.
Titolo autorizzato: Brownian motion, martingales, and stochastic calculus  Visualizza cluster
ISBN: 3-319-31089-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910254069803321
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Serie: Graduate Texts in Mathematics, . 2197-5612 ; ; 274