Probability theory and stochastic processes / Pierre Brémaud.

Format:

Book

Author/Creator:

Brémaud, Pierre, author.

Series:

Universitext

Universitext, 0172-5939

Language:

English

Subjects (All):

Probabilities.

Physical Description:

xvii, 713 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2020]

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.

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. .

Notes:

Includes bibliographical references and index.

Other Format:

Electronic version: Brémaud, Pierre. Probability theory and stochastic processes.

ISBN:

9783030401825

3030401820

OCLC:

1191807646