Coverart for item
The Resource Brownian Motion, Martingales, and Stochastic Calculus, by Jean-François Le Gall, (electronic resource)

Brownian Motion, Martingales, and Stochastic Calculus, by Jean-François Le Gall, (electronic resource)

Label
Brownian Motion, Martingales, and Stochastic Calculus
Title
Brownian Motion, Martingales, and Stochastic Calculus
Statement of responsibility
by Jean-François Le Gall
Creator
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Le Gall, J. F.
Image bit depth
0
Literary form
non fiction
Series statement
Graduate Texts in Mathematics,
Series volume
274
http://library.link/vocab/subjectName
  • Mathematics
  • Measure theory
  • Economics, Mathematical
  • System theory
  • Mathematical models
  • Probabilities
Label
Brownian Motion, Martingales, and Stochastic Calculus, by Jean-François Le Gall, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-31089-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-3-319-31089-3
Dimensions
unknown
Extent
1 online resource (xi, 273 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319310893
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-31089-3
Other physical details
5 illustrations, 1 illustration in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)948681360
Label
Brownian Motion, Martingales, and Stochastic Calculus, by Jean-François Le Gall, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-31089-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-3-319-31089-3
Dimensions
unknown
Extent
1 online resource (xi, 273 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319310893
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-31089-3
Other physical details
5 illustrations, 1 illustration in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)948681360

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