國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Brownian motion, martingales, and st...

Le Gall, Jean-Francois.

Brownian motion, martingales, and stochastic calculus

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Brownian motion, martingales, and stochastic calculusby Jean-Francois Le Gall.
作者:	Le Gall, Jean-Francois.
出版者:	Cham :Springer International Publishing :2016.
面頁冊數:	xi, 273 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Brownian motion processes.
電子資源:	http://dx.doi.org/10.1007/978-3-319-31089-3
ISBN:	9783319310893$q(electronic bk.)

Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-Francois.

Brownian motion, martingales, and stochastic calculus[electronic resource] /by Jean-Francois Le Gall. - Cham :Springer International Publishing :2016. - xi, 273 p. :ill. (some col.), digital ;24 cm. - Graduate texts in mathematics,2740072-5285 ;. - Graduate texts in mathematics ;129..

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.

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 Ito'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 Ito, 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.

ISBN: 9783319310893$q(electronic bk.)

Standard No.: 10.1007/978-3-319-31089-3doiSubjects--Topical Terms:

183837
Brownian motion processes.

LC Class. No.: QA274.75

Dewey Class. No.: 519.233

Brownian motion, martingales, and stochastic calculus
LDR:03016nmm a2200337 a 4500 001 486832
003 DE-He213
005 20161013084550.0
006 m d
007 cr nn 008maaau
008 161116s2016 gw s 0 eng d
020 $a 9783319310893$q(electronic bk.)
020 $a 9783319310886$q(paper)
024 7 $a 10.1007/978-3-319-31089-3 $2 doi
035 $a 978-3-319-31089-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.75
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 519.233 $2 23
090 $a QA274.75 $b .L496 2016
100 1 $a Le Gall, Jean-Francois. $3 745067
245 1 0 $a Brownian motion, martingales, and stochastic calculus $h [electronic resource] / $c by Jean-Francois Le Gall.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xi, 273 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 274
505 0 $a 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.
520 $a 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 Ito'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 Ito, 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.
650 0 $a Brownian motion processes. $3 183837
650 0 $a Martingales (Mathematics) $3 182691
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Quantitative Finance. $3 274071
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
650 2 4 $a Systems Theory, Control. $3 274654
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-31089-3
950 $a Mathematics and Statistics (Springer-11649)