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<図書>
Brownian motion and stochastic calculus

責任表示 Ioannis Karatzas, Steven E. Shreve
シリーズ Graduate texts in mathematics ; 113
データ種別 図書
2nd ed
出版者 New York ; Tokyo : Springer-Verlag
出版年 c1991
本文言語 英語
大きさ xxiii, 470 p. : ill. ; 24 cm
概要 A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for...this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
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所蔵情報


理系図3F 数理独自 068222192001252 SER/GTM/113a 1991

理系図3F 数理独自 068222195010952 KARA/40/1 1994
: us 中央図 自動書庫 017211997019158 423.1/Ka 63/1a 1997
: us 理系図1F 開架 003212005000567 423.1/Ka 63 1998

書誌詳細

一般注記 Bibliography: p. [447]-458
Includes index
著者標目 *Karatzas, Ioannis
Shreve, Steven E.
件 名 LCSH:Brownian motion processes
LCSH:Stochastic analysis
分 類 LCC:QA274.75
DC20:530.4/75
NDC9:417.1
NDC8:423.1
書誌ID 1000030368
ISBN 0387976558
NCID BA1316430X
巻冊次 : us ; ISBN:0387976558
: gw ; ISBN:3540976558
登録日 2009.09.10
更新日 2017.02.18

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