Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics) (Graduate Texts in Mathematics, 113)

IoannisKaratzas

• Springer (1997年6月20日発売)

作品紹介・あらすじ

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.

感想・レビュー・書評

[Singappさんの感想 · 2021年12月4日]

ファイナンスのための確率II

[ufosummerさんの感想 · 2014年8月31日]

色々載っている。

[laughtingmanさんの感想 · 2009年9月19日]

確率微分方程式

修士時代（M1）のセミナのテキスト
誤植が驚くほど少ない！古めの論文のmainResultがExerciseとかProblemになってたりするから侮れない。
その道に精通した指導者の下で読むことが前提になっているので
相当この分野に親しんでない限り独学には不向き。
離散Martingaleと函数解析の初歩くらいまでは自在に使いこなせるのが
必須条件。