Stochastic Analysis (eBook)
XII, 218 Seiten
Springer Singapore (Verlag)
978-981-15-8864-8 (ISBN)
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.
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.
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 ofthe 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.
Erscheint lt. Verlag | 20.10.2020 |
---|---|
Reihe/Serie | Monographs in Mathematical Economics | Monographs in Mathematical Economics |
Zusatzinfo | XII, 218 p. 1 illus. |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Statistik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | Applications to Mathematical Finances • Brownian motions • Euler--Maruyama Approximations • Martingale for Continuous Time Parameters • Stochastic differential equations • stochastic integrals |
ISBN-10 | 981-15-8864-3 / 9811588643 |
ISBN-13 | 978-981-15-8864-8 / 9789811588648 |
Haben Sie eine Frage zum Produkt? |
![PDF](/img/icon_pdf_big.jpg)
Größe: 2,1 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich