Stochastic Analysis

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الناشر	Springer; 1st ed. 2020 edition
رقم الكتاب المعياري الدولي 10	981158866X
تنسيق الكتاب	Paperback
وصف الكتاب	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.
عدد الصفحات	232 pages

رقم الكتاب المعياري الدولي 13	9789811588662
الكاتب	Shigeo Kusuoka
اللغة	English
عن المؤلف	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. Read more