| 书目名称 | Measure Theory, Probability, and Stochastic Processes | | 编辑 | Jean-François Le Gall | | 视频video | | | 概述 | Provides a rigorous treatment of measure theory geared towards the general theory of stochastic processes.Highlights the interplay between probability and other areas of mathematics such as complex va | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | .This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis..Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selectionof illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.. .Measure Theory, Probability, and Stoch | | 出版日期 | Textbook 2022 | | 关键词 | probability le gall; rigorous probability textbook; probability measure textbook; measure theory for pr | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-14205-5 | | isbn_softcover | 978-3-031-14207-9 | | isbn_ebook | 978-3-031-14205-5Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:12:54
