Brownian motion, martingales, and stochastic calculus:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
[Cham]
Springer
[2016]
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Schriftenreihe: | Graduate texts in mathematics
274 |
Schlagworte: | |
Online-Zugang: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 URL des Erstveröffentlichers Inhaltsverzeichnis Abstract |
Beschreibung: | 1 Online-Ressource (xiii, 273 Seiten) Illustrationen, Diagramme |
ISBN: | 9783319310893 |
ISSN: | 0072-5285 |
DOI: | 10.1007/978-3-319-31089-3 |
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Datensatz im Suchindex
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adam_text | BROWNIAN MOTION, MARTINGALES, AND STOCHASTIC CALCULUS
/ LE GALL, JEAN-FRANCOIS
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
BROWNIAN MOTION, MARTINGALES, AND STOCHASTIC CALCULUS
/ LE GALL, JEAN-FRANCOIS
: 2016
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
author | Le Gall, Jean-François 1959- |
author_GND | (DE-588)1033682829 |
author_facet | Le Gall, Jean-François 1959- |
author_role | aut |
author_sort | Le Gall, Jean-François 1959- |
author_variant | g j f l gjf gjfl |
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collection | ZDB-2-SMA |
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dewey-full | 519.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-3-319-31089-3 |
format | Electronic eBook |
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isbn | 9783319310893 |
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series2 | Graduate texts in mathematics |
spelling | Le Gall, Jean-François 1959- (DE-588)1033682829 aut Brownian motion, martingales, and stochastic calculus Jean-François Le Gall [Cham] Springer [2016] © 2016 1 Online-Ressource (xiii, 273 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 274 0072-5285 Mathematics Measure theory Economics, Mathematical System theory Mathematical models Probabilities Probability Theory and Stochastic Processes Quantitative Finance Measure and Integration Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematisches Modell Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Martingal (DE-588)4126466-6 s Stochastische Analysis (DE-588)4132272-1 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-3-319-31088-6 Erscheint auch als Druck-Ausgabe, Paperback 978-3-319-80961-8 Graduate texts in mathematics 274 (DE-604)BV035421258 274 https://doi.org/10.1007/978-3-319-31089-3 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961632&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
spellingShingle | Le Gall, Jean-François 1959- Brownian motion, martingales, and stochastic calculus Graduate texts in mathematics Mathematics Measure theory Economics, Mathematical System theory Mathematical models Probabilities Probability Theory and Stochastic Processes Quantitative Finance Measure and Integration Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematisches Modell Brownsche Bewegung (DE-588)4128328-4 gnd Martingal (DE-588)4126466-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
subject_GND | (DE-588)4128328-4 (DE-588)4126466-6 (DE-588)4132272-1 |
title | Brownian motion, martingales, and stochastic calculus |
title_auth | Brownian motion, martingales, and stochastic calculus |
title_exact_search | Brownian motion, martingales, and stochastic calculus |
title_full | Brownian motion, martingales, and stochastic calculus Jean-François Le Gall |
title_fullStr | Brownian motion, martingales, and stochastic calculus Jean-François Le Gall |
title_full_unstemmed | Brownian motion, martingales, and stochastic calculus Jean-François Le Gall |
title_short | Brownian motion, martingales, and stochastic calculus |
title_sort | brownian motion martingales and stochastic calculus |
topic | Mathematics Measure theory Economics, Mathematical System theory Mathematical models Probabilities Probability Theory and Stochastic Processes Quantitative Finance Measure and Integration Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematisches Modell Brownsche Bewegung (DE-588)4128328-4 gnd Martingal (DE-588)4126466-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
topic_facet | Mathematics Measure theory Economics, Mathematical System theory Mathematical models Probabilities Probability Theory and Stochastic Processes Quantitative Finance Measure and Integration Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematisches Modell Brownsche Bewegung Martingal Stochastische Analysis |
url | https://doi.org/10.1007/978-3-319-31089-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961632&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV035421258 |
work_keys_str_mv | AT legalljeanfrancois brownianmotionmartingalesandstochasticcalculus |