#stochastic-processes

60. Probability Theory and Stochastic Processes

This volume develops probability theory on measure-theoretic foundations and studies stochastic processes. It emphasizes rigor, structure, and applications. Part I. Foundations of Probability Chapter 1. Probability Spaces 1.1 Sigma-algebras and events 1.2 Probability measures 1.3 Examples 1.4 Basic properties 1.5 Interpretations Chapter 2. Random Variables 2.1 Definitions 2.2 Distributions 2.3 Expectation 2.4 Variance 2.5 Examples Chapter 3. Independence 3.1 Independent events 3.2 Independent random variables 3.3 Conditional probability 3.4 Conditional...