Introduction to Probability Theory and Stochastic Processes - Hardcover

Chiasson, John

 
9781118382790: Introduction to Probability Theory and Stochastic Processes
Hardcover
ISBN 10: 111838279X ISBN 13: 9781118382790
Verlag: Wiley, 2013

Inhaltsangabe

A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications
 
This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.
 
Features include:
* The theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18)
* Coverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena
* Explicit construction of continuous random variables to facilitate the "digestion" of random variables, i.e., how they are used in contrast to how they are defined
* Explicit construction of continuous random variables to facilitate the two views of expectation: as integration over the underlying probability space (abstract view) or as integration using the density function (usual view)
* A discussion of the connections between Bernoulli, geometric, and Poisson processes
* Incorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance
 
Comprehensive, astute, and practical, Introduction to Probability Theory and Stochastic Processes is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

JOHN CHIASSON, PhD, is a Fellow of the IEEE and the author of Modeling and High-Performance Control of Electric Machines, published by Wiley-IEEE Press.

Von der hinteren Coverseite

A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications
 
This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.
 
Features include:
* The theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18)
* Coverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena
* Explicit construction of continuous random variables to facilitate the "digestion" of random variables, i.e., how they are used in contrast to how they are defined
* Explicit construction of continuous random variables to facilitate the two views of expectation: as integration over the underlying probability space (abstract view) or as integration using the density function (usual view)
* A discussion of the connections between Bernoulli, geometric, and Poisson processes
* Incorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance
 
Comprehensive, astute, and practical, Introduction to Probability Theory and Stochastic Processes is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.

Aus dem Klappentext

A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications

This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.

Features include:

  • The theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18)
  • Coverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena
  • Explicit construction of continuous random variables to facilitate the "digestion" of random variables, i.e., how they are used in contrast to how they are defined
  • Explicit construction of continuous random variables to facilitate the two views of expectation: as integration over the underlying probability space (abstract view) or as integration using the density function (usual view)
  • A discussion of the connections between Bernoulli, geometric, and Poisson processes
  • Incorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance

Comprehensive, astute, and practical, Introduction to Probability Theory and Stochastic Processes is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Wiley
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
111838279X
ISBN 13 
9781118382790
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
984
Kontakt zum Hersteller
Wiley-VCH GmbH
product_safety@wiley.com

Boschstrasse 12
Weinheim
69469
Deutschland