This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.
The initial chapters provide a rigorous introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Stein's method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The Itô-Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods.
Based on courses taught by the authors, this book can serve as the main text for a graduate-level course on probability, and each chapter contains a collection of exercises. The unique combination of probability and functional analysis, as well as the advanced and original topics included, will also appeal to researchers working in probability and related fields.
| ISBN: | 9783031840661 |
| Publication date: | 26th March 2025 |
| Author: | Hannah Geiss, Stefan Geiss |
| Publisher: | Springer an imprint of Springer Nature Switzerland |
| Format: | Paperback |
| Pagination: | 443 pages |
| Series: | Universitext |
| Genres: |
Probability and statistics Stochastics Functional analysis and transforms Integral calculus and equations |
This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.
The initial chapters provide a rigorous introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Stein's method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The Itô-Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods.
Based on courses taught by the authors, this book can serve as the main text for a graduate-level course on probability, and each chapter contains a collection of exercises. The unique combination of probability and functional analysis, as well as the advanced and original topics included, will also appeal to researchers working in probability and related fields.
Measure, Probability and Functional Analysis features in the following genres: Probability and statistics, Stochastics, Functional analysis and transforms, Integral calculus and equations
Measure, Probability and Functional Analysis is available in Paperback
Measure, Probability and Functional Analysis was written by Hannah Geiss, Stefan Geiss and published by Springer an imprint of Springer Nature Switzerland
Measure, Probability and Functional Analysis has 443 pages
Yes it is part of Universitext series
£49.49