Probability theory and stochastic processes
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes …
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- Full title :Probability theory and stochastic processes / Pierre Brémaud.
Summary
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.
Read More ↓Edition Statements
- Publication Date:©2020
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:xvii, 713 pages : 24 cm
Edition Identifiers
- ISBN:9783030401825, 3030401820
- oclc:on1154463189
- LC Classification:QA273
- Dewey Decimal:519.2
Table of Contents
Introduction.-Warming Up -- Integration Theory for Probability -- Probability and Expectation -- Convergence of random sequences -- Markov Chains -- Martingale Sequences -- Ergodic Sequences -- Generalities on Stochastic Processes -- Poisson Processes -- Continuous-Time Markov Chains -- Renewal Theory in Continuous Time -- Brownian Motion -- Wide-sense Stationary Stochastic Processes -- An Introduction to Itô's Calculus -- Appenndix: Number Theory and Linear Algebra -- Analysis -- Hilbert Spaces -- Z-Transforms -- Proof of Paul Lévy's Criterion -- Direct Riemann Integrability -- Bibliography -- Index.
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