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Monographs in Mathematical Economics

Stochastic Analysis

Authors: Kusuoka, Shigeo

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  • Defines conditional exceptions differently than in other books
  • Uses only elementary facts for proof of the Doob–Meyer decomposition theorem for special cases
  • Shows how the Euler–Maruyama approximation plays an important role in proving the uniqueness of martingale problems 
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eBook $89.00
price for USA in USD
  • ISBN 978-981-15-8864-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-981-15-8863-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas.

In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations. 

About the authors

The author is currently Professor Emeritus at The University of Tokyo and visiting Professor at Meiji University. He previously held positions at The University of Tokyo and Research Institute for Mathematical Sciences, Kyoto University. He was an invited speaker at the ICM 1990.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-981-15-8864-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-981-15-8863-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Analysis
Authors
Series Title
Monographs in Mathematical Economics
Series Volume
3
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-8864-8
DOI
10.1007/978-981-15-8864-8
Hardcover ISBN
978-981-15-8863-1
Series ISSN
2364-8279
Edition Number
1
Number of Pages
XII, 218
Number of Illustrations
1 b/w illustrations
Topics