Stochastic Calculus and Applications (2nd Edition)

Download Stochastic Calculus and Applications (2nd Edition) written by Samuel N. Cohen, Robert J. Elliott in PDF format. This book is under the category Calculus and bearing the isbn/isbn13 number 149392866X; 1493936816/9781493928668/ 9781493936816. You may reffer the table below for additional details of the book.


SKU: 573eec40e4ef Category: Tags: ,



Samuel N. Cohen, Robert J. Elliott


Birkhäuser; 2nd Edition




666 pages






149392866X; 1493936816


9781493928668/ 9781493936816

Book Description

The modern general theory of random processes and stochastic integrals is utilized by electronic engineers, systems theorists, and more recently, those working in mathematical and quantitative finance. This completely revised and significantly expanded second edition of Stochastic Calculus and Applications (PDF) takes readers who have only been exposed to fundamental courses in analysis through the modern general theory of random processes and stochastic integrals. Building upon the first publication of this title, this ebook will be of great interest to graduate students, research mathematicians working in those subjects, quants working in the finance business, and other related professionals.

The following are some of the new features included in this second edition:

New chapters on fundamental measure theory, together with exercises at the chapter’s end and backward stochastic differential equations reworked proofs, examples, and additional material for explanation; a heightened emphasis on the importance of being motivated by mathematics; Comprehensive index of subjects covered.


“This is a fundamental ebook in modern stochastic calculus and its applications: rich contents; well-structured material; comprehensive coverage of all important results given with complete proofs and well illustrated by examples; carefully written text.” “This is a fundamental ebook in modern stochastic calculus and its applications: rich contents; well-structured material; comprehensive coverage of all important results given with complete proofs As a result, there are numerous arguments that are more than sufficient to recommend the ebook to a large number of people. There are highly-motivated and capable graduate school students counted among them. Additionally, the e-book makes for a fantastic research tool.” — Jordan M. Stoyanov; zbMATH 1338.60001; 2016

“Such a comprehensive and self-contained presentation of stochastic calculus and applications addresses an existing need in the literature,” the author explains. The e-book is a good resource for students in their first year of graduate school. It will be helpful for anyone who intended to deal with stochastic calculus as well as any applications of it. — Zentralblatt

PLEASE TAKE NOTE That the only thing that is included in the purchase is the PDF version of the ebook “Stochastic Calculus and Applications, 2nd Edition.” There are no access codes contained within.

Table of contents

Table of contents :
Front Matter….Pages i-xxiii
Front Matter….Pages 1-1
Measure and Integral….Pages 3-47
Probabilities and Expectation….Pages 49-69
Front Matter….Pages 71-71
Filtrations, Stopping Times and Stochastic Processes….Pages 73-87
Martingales in Discrete Time….Pages 89-107
Martingales in Continuous Time….Pages 109-137
The Classification of Stopping Times….Pages 139-151
The Progressive, Optional and Predictable σ-Algebras….Pages 153-171
Front Matter….Pages 173-173
Processes of Finite Variation….Pages 175-197
The Doob–Meyer Decomposition….Pages 199-210
The Structure of Square Integrable Martingales….Pages 211-232
Quadratic Variation and Semimartingales….Pages 233-258
The Stochastic Integral….Pages 259-292
Random Measures….Pages 293-334
Front Matter….Pages 335-335
Itô’s Differential Rule….Pages 337-365
The Exponential Formula and Girsanov’s Theorem….Pages 367-396
Lipschitz Stochastic Differential Equations….Pages 397-426
Markov Properties of SDEs….Pages 427-450
Weak Solutions of SDEs….Pages 451-465
Backward Stochastic Differential Equations….Pages 467-493
Front Matter….Pages 495-495
Control of a Single Jump….Pages 497-516
Front Matter….Pages 495-495
Optimal Control of Drifts and Jump Rates….Pages 517-534
Filtering….Pages 535-566
Back Matter….Pages 567-666

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