论文标题
关于概率理论的讲座
Lectures on Probability Theory
论文作者
论文摘要
这些是2014年春季和2015年春季苏黎世大学写的讲义。笔记的第一部分给出了概率理论的介绍。它解释了随机事件和随机变量，概率度量，期望，分布，特征功能，随机变量的独立性，收敛类型和限制定理的概念。第一部分分为两个不同的章节。第一章是关于概率理论的组合方面，第二章是概率理论的实际介绍，其中包含现代概率语言。第二部分涵盖了有条件的期望，马尔丁加尔和马尔可夫连锁店，在阅读第一部分后，它们很容易获得。这些章节完全涵盖了此顺序，并详细介绍了各自主题的更多细节。
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables, probability measures, expectation, distributions, characteristic function, independence of random variables, types of convergence and limit theorems. The first part is separated into two different chapters. The first chapter is about combinatorial aspects of probability theory and the second chapter is the actual introduction to probability theory, which contains the modern probability language. The second part covers conditional expectations, martingales and Markov chains, which are easily accessible after reading the first part. The chapters are exactly covered in this order and go into some more details of the respective topic.
