Mathematical models of information and stochastic systems. (2018)

• Record Type: Book
• Further Information: Note: Philipp Kornreich.
• Other Names: Kornreich, Philipp
• Contents: PREFACE ; Introduction ; Historical Development and Aspects of Probability Theory; Discussion of the Material in This Text; References; Events and Density of Events ; General Probability Concepts; Probabilities of Continuous Sets of Events; Discrete Events Having the Same Probability; Digression of Factorials and the Γ Function; Continuous Sets of Events Having the Same Probability, Density of States; Problems; Joint, Conditional, and Total Probabilities Conditional Probabilities; Dependent, Independent, and Exclusive Events; Total Probability and Bayes’ Theorem of Discrete Events; Markov Processes; Joint, Conditional, and Total Probabilities and Bayes’ Theorem of Continuous Events; Problems; Random Variables and Functions of Random Variables ; Concept of a Random Variable and Functions of a Random Variable; Discrete Distribution Functions; Discrete Distribution Functions for More Than One Value of a Random Variable with the Same Probability; Continuous Distribution and Density Functions; Continuous Distribution Functions for More Than One Value of a Random Variable with the Same Probability; Discrete Distribution Functions of Multiple Random Variables; Continuous Distribution Functions of Multiple Random Variables; Phase Space, a Special Case of Multiple Random Variables; Problems; Conditional Distribution Functions and a Special Case: The Sum of Two Random Variables ; Discrete Conditional Distribution Functions; Continuous Conditional Distribution Functions; A Special Case: The Sum of Two Statistically Independent Discrete Random Variables; A Special Case: The Sum of Two Statistically Independent Continuous Random Variables; Problems; Average Values, Moments, and Correlations of Random Variables and of Functions of Random Variables ; The Most Likely Value of a Random Variable; The Average Value of a Discrete Random Variable and of a Function of a Discrete Random Variable; An Often-Used Special Case; The Probabilistic Mathematical Model of Discrete Quantum Mechanics; The Average Value of a Continuous Random Variable and of a Function of a Continuous Random Variable; The Probabilistic Model of Continuous Quantum Mechanics; Moments of Random Variables; Conditional Average Value of a Random Variable and of a Function of a Random Variable; Central Moments; Variance and Standard Deviation; Correlations of Two Random Variables and of Functions of Random Variables; A Special Case: The Average Value of e−jkx ; References; Problems; Randomness and Average Randomness ; The Concept of Randomness of Discrete Events; The Concept of Randomness of Continuous Events; The Average Randomness of Discrete Events; The Average Randomness of Continuous Random Variables; The Average Randomness of Random Variables with Values That Have the Same Probability; The Entropy of Real Physical Systems and a Very Large Number; The Cepstrum; Stochastic Temperature and the Legendre Transform; Other Stochastic Potentials and the Noise Figure; References; Problems; Most Random Systems ; Methods for Determining Probabilities; Determining Probabilities Based on What Is Known about a System; The Poisson Probability and One of Its Applications; Continuous Most Random Systems; Properties of Gaussian Stochastic Systems; Important Examples of Stochastic Physical Systems; The Limit of Zero and Very Large Temperatures; References; Problems; Information ; Information; Information in Genes; Information Transmission of Discrete Systems; Information Transmission of Continuous or Analog Systems; The Maximum Information and Optimum Transmission Rates of Discrete Systems; The Maximum Information and Optimum Transmission Rates of Continuous or Analog Systems; The Bit Error Rate; References; Problems; Random Processes ; Random Processes; Random Walk and the Famous Case of Scent Molecules Emerging from a Perfume Bottle; The Simple Stochastic Oscillator and Clocks; Correlation Functions of Random Processes; Stationarity of Random Processes; The Time Average and Ergodicity of Random Processes; Partially Coherent Light Rays as Random Processes; Stochastic Aspects of Transitions between States; Cantor Sets as Random Processes; References; Problems; Spectral Densities ; Stochastic Power; The Power Spectrum and Cross-Power Spectrum; The Effects of Filters on the Autocorrelation Function and the Power Spectral Density; The Bandwidth of the Power Spectrum ; Problems; Data Analysis ; Least Square Differences; The Special Case of Linear Regression; Other Examples; Problems; Chaotic Systems ; Fractals; Mandelbrot Sets; Difference Equations; The Hénon Difference Equation; Single-Particle Single-Well Potential; References; INDEX
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2018
• Extent: 1 online resource (376 pages), (124 illustrations)
• Subjects: 003.76015118; Stochastic systems -- Mathematical models; System analysis -- Mathematical models
• Languages: English
• ISBNs: 9781351835046; 1351835041
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.