An introduction to applied probability

Bibliographic Information

An introduction to applied probability

Pierre Brémaud

(Texts in applied mathematics, 77)

Springer, c2024

  • : hbk

Available at  / 3 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 487) and index

Description and Table of Contents

Description

This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences. The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above. The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models: Markov chains, which are omnipresent and versatile models in applied probability Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks Brownian motion, which models fluctuations in the stock market and the "white noise" of physics Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences. This book can be used as a text in various ways and at different levels of study. Essentially, it provides the material for a two-semester graduate course on probability and stochastic processes in a department of applied mathematics or for students in departments where stochastic models play an essential role. The progressive introduction of concepts and tools, along with the inclusion of numerous examples, also makes this book well-adapted for self-study.

Table of Contents

Preface.- Basic Notions.- Discrete Random Variables.- Continuous Random Vectors.- The Lebesgue Integral.- From Integral to Expectation.- Convergence Almost Sure.- Convergence in Distribution.- Martingales.- Markov Chains.- Poisson Processes.- Brownian Motion.- Wide-sense Stationary Processes.-  A Review of Hilbert Spaces.- Bibliography.- Index.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BD07312572
  • ISBN
    • 9783031493058
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xiii, 492 p.
  • Size
    25 cm
  • Parent Bibliography ID
Page Top