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A Graduate Course in Probability by LIVIU I NICOLAESCU is a nonfiction available to read on EtoBox.

What is A Graduate Course in Probability about?

Contents Introduction Notation and conventions 1. Foundations 1.1 Measurable spaces 1.1.1 Sigma-algebras 1.1.2 Measurable maps 1.2 Measures and integration 1.2.1 Measures 1.2.2 Independence and conditional probability 1.2.3 Integration of measurable functions 1.2.4 Lp spaces 1.2.5 Measures on compact metric spaces 1.3 Invariants of random variables 1.3.1 The distribution and the expectation of a random variable 1.3.2 Higher order integral invariants of random variables 1.3.3 Classical examples of discrete random variables 1.3.4 Classical examples of continuous probability distributions 1.3.5 Product probability spaces and independence 1.3.6 Convolutions of Borel measures on the real axis 1.3.7 Modes of convergence of random variables 1.4 Conditional expectation 1.4.1 Conditioning on a sigma sub-algebra 1.4.2 Some applications of conditioning 1.4.3 Conditional independence 1.4.4 Kernels and regular conditional distributions 1.4.5 Disintegration of measures 1.5 What are stochastic processes? 1.5.1 Definition and examples 1.5.2 Kolmogorov's existence theorem 1.6 Exercises 2. Limit theorems 2.1 The Law of Large Numbers 2.1.1 Random series 2.1.2 The Law of Large Numbers 2.1.3 Entropy an

Who reads A Graduate Course in Probability?

Author

LIVIU I NICOLAESCU

Publisher

World Scientific Publishing

Published

2023

Language

EN

ISBN

9789811255083

Category

nonfiction