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Mathematical Models Of Information And Stochastic Systems.

Mathematical Models Of Information And Stochastic Systems.

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  • ISBN:9781420058833
  • Editorial: Crc Press Inc.
  • Fecha de la edición:
  • Encuadernación:Tapa dura
  • Dimensiones: 0 cm x 0 cm
  • Nº Pág.:364
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From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties.

After an introduction, the book presents several basic principles that are employed in the remainder of the text to develop useful examples of probability theory. It examines both discrete and continuous distribution functions and random variables, followed by a chapter on the average values, correlations, and covariances of functions of variables as well as the probabilistic mathematical model of quantum mechanics. The author then explores the concepts of randomness and entropy and derives various discrete probabilities and continuous probability density functions from what is known about a particular stochastic system. The final chapters discuss information of discrete and continuous systems, time-dependent stochastic processes, data analysis, and chaotic systems and fractals.

Ch. 1 Introduction 1
Ch. 2 Events and Density of Events 9
Ch. 3 Joint, Conditional, and Total Probabilities 41
Ch. 4 Random Variables and Functions of Random Variables 61
Ch. 5 Conditional Distribution Functions and a Special Case: The Sum of Two Random Variables 83
Ch. 6 Average Values, Moments, and Correlations of Random Variables and of Functions of Random Variables 99
Ch. 7 Randomness and Average Randomness 149
Ch. 8 Most Random Systems 181
Ch. 9 Information 241
Ch. 10 Random Processes 279
Ch. 11 Spectral Densities 315
Ch. 12 Data Analysis 329
Ch. 13 Chaotic Systems 337

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