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Cover: 9789811588631 | Stochastic Analysis | Shigeo Kusuoka | Buch | xii | Englisch | 2020
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Stochastic Analysis
Buch von Shigeo Kusuoka
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
Chapter ¿1. Preparations from probability theory.- Chapter 2. Martingale with discrete parameter.- Chapter 3. Martingale with continuous parameter.- Chapter 4. Stochastic integral.- Chapter 5. Applications of stochastic integral.- Chapter 6. Stochastic differential equation.- Chapter 7. Application to finance.- Chapter 8. Appendices.- References.
Details
Erscheinungsjahr: 2020
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Monographs in Mathematical Economics
Inhalt: xii
218 S.
1 s/w Illustr.
218 p. 1 illus.
ISBN-13: 9789811588631
ISBN-10: 9811588635
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kusuoka, Shigeo
Auflage: 1st ed. 2020
Hersteller: Springer Singapore
Springer Nature Singapore
Monographs in Mathematical Economics
Maße: 241 x 160 x 19 mm
Von/Mit: Shigeo Kusuoka
Erscheinungsdatum: 20.10.2020
Gewicht: 0,518 kg
Artikel-ID: 118908808
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
Chapter ¿1. Preparations from probability theory.- Chapter 2. Martingale with discrete parameter.- Chapter 3. Martingale with continuous parameter.- Chapter 4. Stochastic integral.- Chapter 5. Applications of stochastic integral.- Chapter 6. Stochastic differential equation.- Chapter 7. Application to finance.- Chapter 8. Appendices.- References.
Details
Erscheinungsjahr: 2020
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Monographs in Mathematical Economics
Inhalt: xii
218 S.
1 s/w Illustr.
218 p. 1 illus.
ISBN-13: 9789811588631
ISBN-10: 9811588635
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kusuoka, Shigeo
Auflage: 1st ed. 2020
Hersteller: Springer Singapore
Springer Nature Singapore
Monographs in Mathematical Economics
Maße: 241 x 160 x 19 mm
Von/Mit: Shigeo Kusuoka
Erscheinungsdatum: 20.10.2020
Gewicht: 0,518 kg
Artikel-ID: 118908808
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