Overview
- Unique resource for rigorous study of stochastic integration theory, discontinuous processes, and many applications in filtering and control
- Useful for a wide range of researchers, practicioners, and students in mathematics, statistics, and engineering Updated and revised to approach topics with a modern perspective
- New edition includes end of chapter exercises, new chapters, reworked examples, and an extensive topical index
Part of the book series: Probability and Its Applications (PA)
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Table of contents (22 chapters)
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Front Matter
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Measure Theoretic Probability
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Front Matter
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Stochastic Differential Equations
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Front Matter
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Keywords
About this book
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry.
New features of this edition include:
End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index.
"Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)
Reviews
“As supplementary reading for a second course or as s comprehensive (!) resource for the general theory of processes aimed at Ph. D. students and scholars, this second edition will stay a valuable resource.” (René L. Schilling, Mathematical Reviews, October, 2016)
“This is a fundamental book in modern stochastic calculus and its applications: rich contents, well structured material, comprehensive coverage of all significant results given with complete proofs and well illustrated by examples, carefully written text. Hence, there are more than enough reasons to strongly recommend the book to a wide audience. Among them, there are good and motivated graduate university students. … Also, the book is an excellent reference book.” (Jordan M. Stoyanov, zbMATH 1338.60001, 2016)
Authors and Affiliations
About the authors
Samuel N. Cohen is an Associate Professor in the Mathematical Institute at the University of Oxford, an associate member of the Oxford-Man Institute for Quantitative Finance and a member of the Oxford-Nie Financial Big Data Laboratory. He has a Ph.D. in Mathematics from the University of Adelaide, along with undergraduate degrees in Mathematics and Finance.
Robert Elliott received Bachelors and Masters degrees from Oxford University, and his Ph.D. and D.Sc. from the University of Cambridge. He has held positions at Newcastle, Yale, Oxford, Warwick, Hull, Alberta, Calgary and Adelaide, and visiting positions in Toronto, Northwestern, Kentucky, Brown, Paris, Denmark, Hong Kong and Australia. From 2001 to 2009 he was the RBC Financial Group Professor of Finance at the University of Calgary, Canada, where he was also an Adjunct Professor in both the Department of Mathematics and the Department of Electrical Engineering. From 2009 to 2013 he was an Australian Professorial Fellow atthe University of Adelaide. Professor Elliott has authored nine books and over 450 papers.
Bibliographic Information
Book Title: Stochastic Calculus and Applications
Authors: Samuel N. Cohen, Robert J. Elliott
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/978-1-4939-2867-5
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2015
Hardcover ISBN: 978-1-4939-2866-8Published: 19 November 2015
Softcover ISBN: 978-1-4939-3681-6Published: 19 November 2015
eBook ISBN: 978-1-4939-2867-5Published: 18 November 2015
Series ISSN: 2297-0371
Series E-ISSN: 2297-0398
Edition Number: 2
Number of Pages: XXIII, 666
Additional Information: Previously published with Springer, 1982. Springer series "Applications of Mathematics". New originator (Samuel N. Cohen) added for second edition.
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations, Electrical Engineering, Computational Mathematics and Numerical Analysis, Quantitative Finance