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An Introduction to Applied Probability de Pierre Brémaud

An Introduction to Applied Probability: Texts in Applied Mathematics, cartea 77

Autor Pierre Brémaud
en Limba Engleză Hardback – 4 mai 2024
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.
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Specificații

ISBN-13: 9783031493058
ISBN-10: 3031493052
Pagini: 492
Ilustrații: XIII, 492 p.
Dimensiuni: 155 x 235 mm
Greutate: 1 kg
Ediția:2024
Editura: Springer International Publishing
Colecția Springer
Seria Texts in Applied Mathematics

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

Pierre Brémaud graduated from the École Polytechnique and obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science at the University of California, Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference books and textbooks.

Textul de pe ultima copertă

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 the efficient 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.

Caracteristici

Provides a clear and intuitive introduction to the range of probabilistic tools used in the applied sciences Covers diverse topics such as random graphs, rejection sampling, and Bayesian hypothesis testing Includes lots of exercises for practice and homework