Mouvement Brownien, Martingales Et Calcul Stochastique
| AUTHOR | Le Gall, Jean-Francois |
| PUBLISHER | Springer (09/18/2012) |
| PRODUCT TYPE | Paperback (Paperback) |
Cet ouvrage propose une approche concise mais compl te de la th orie de l'int grale stochastique dans le cadre g n ral des semimartingales continues. Apr s une introduction au mouvement brownien et ses principales propri t s, les martingales et les semimartingales continues sont pr sent es en d tail avant la construction de l'int grale stochastique. Les outils du calcul stochastique, incluant la formule d'It , le th or me d'arr t et de nombreuses applications, sont trait s de mani re rigoureuse. Le livre contient aussi un chapitre sur les processus de Markov et un autre sur les quations diff rentielles stochastiques, avec une preuve d taill e des propri t s markoviennes des solutions. De nombreux exercices permettent au lecteur de se familiariser avec les techniques du calcul stochastique.
This book offers a rigorous and self-contained approach to the theory of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including It 's formula, the optional stopping theorem and the Girsanov theorem are treated in detail including many important applications. Two chapters are devoted to general Markov processes and to stochastic differential equations, with a complete derivation of Markovian properties of solutions in the Lipschitz case. Numerous exercises help the reader to get acquainted with the techniques of stochastic calculus.
This book offers a rigorous and self-contained approach to the theory of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including It's formula, the optional stopping theorem and the Girsanov theorem are treated in detail including many important applications. Two chapters are devoted to general Markov processes and to stochastic differential equations, with a complete derivation of Markovian properties of solutions in the Lipschitz case. Numerous exercises help the reader to get acquainted with the techniques of stochastic calculus.
Cet ouvrage propose une approche concise mais compl te de la th orie de l'int grale stochastique dans le cadre g n ral des semimartingales continues. Apr s une introduction au mouvement brownien et ses principales propri t s, les martingales et les semimartingales continues sont pr sent es en d tail avant la construction de l'int grale stochastique. Les outils du calcul stochastique, incluant la formule d'It , le th or me d'arr t et de nombreuses applications, sont trait s de mani re rigoureuse. Le livre contient aussi un chapitre sur les processus de Markov et un autre sur les quations diff rentielles stochastiques, avec une preuve d taill e des propri t s markoviennes des solutions. De nombreux exercices permettent au lecteur de se familiariser avec les techniques du calcul stochastique.
This book offers a rigorous and self-contained approach to the theory of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including It 's formula, the optional stopping theorem and the Girsanov theorem are treated in detail including many important applications. Two chapters are devoted to general Markov processes and to stochastic differential equations, with a complete derivation of Markovian properties of solutions in the Lipschitz case. Numerous exercises help the reader to get acquainted with the techniques of stochastic calculus.