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Brownian Motion, Martingales, and Stochastic Calculus

Af: Jean-Francois Le Gall Engelsk Hardback

Brownian Motion, Martingales, and Stochastic Calculus

Af: Jean-Francois Le Gall Engelsk Hardback
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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.
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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.
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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 273
ISBN-13: 9783319310886
Indbinding: Hardback
Udgave:
ISBN-10: 3319310887
Kategori: Kybernetik og systemteori
Udg. Dato: 9 maj 2016
Længde: 22mm
Bredde: 162mm
Højde: 241mm
Forlag: Springer International Publishing AG
Oplagsdato: 9 maj 2016
Forfatter(e): Jean-Francois Le Gall
Forfatter(e) Jean-Francois Le Gall

Kategori Kybernetik og systemteori

ISBN-13 9783319310886

Sprog Engelsk

Indbinding Hardback

Sider 273

Udgave

Længde 22mm

Bredde 162mm

Højde 241mm

Udg. Dato 9 maj 2016

Oplagsdato 9 maj 2016

Forlag Springer International Publishing AG

Kategori sammenhænge