國立虎尾科技大學 |

Brownian Motion, Martingales, and Stochastic Calculus

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Brownian Motion, Martingales, and Stochastic Calculus / by Jean-François Le Gall.
作者:	Le Gall, Jean-François.
面頁冊數:	XIII, 273 p. 5 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-319-31089-3
ISBN:	9783319310893

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

Brownian Motion, Martingales, and Stochastic Calculus [electronic resource] /by Jean-François Le Gall. - 1st ed. 2016. - XIII, 273 p. 5 illus., 1 illus. in color.online resource. - Graduate Texts in Mathematics,2740072-5285 ;. - Graduate Texts in Mathematics,222.

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 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.

ISBN: 9783319310893

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

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Brownian Motion, Martingales, and Stochastic Calculus
LDR:03468nam a22004335i 4500 001 978447
003 DE-He213
005 20200704073944.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319310893 $9 978-3-319-31089-3
024 7 $a 10.1007/978-3-319-31089-3 $2 doi
035 $a 978-3-319-31089-3
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Le Gall, Jean-François. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1271890
245 1 0 $a Brownian Motion, Martingales, and Stochastic Calculus $h [electronic resource] / $c by Jean-François Le Gall.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XIII, 273 p. 5 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 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.
650 0 $a Probabilities. $3 527847
650 0 $a Economics, Mathematical . $3 1253712
650 0 $a Measure theory. $3 527848
650 0 $a Mathematical models. $3 527886
650 0 $a System theory. $3 566168
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Quantitative Finance. $3 669372
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 669172
650 2 4 $a Systems Theory, Control. $3 669337
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319310886
776 0 8 $i Printed edition: $z 9783319310909
776 0 8 $i Printed edition: $z 9783319809618
830 0 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222 $3 1254915
856 4 0 $u https://doi.org/10.1007/978-3-319-31089-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)