Principles of Statistical Radiophysics 1

1. General Introduction.- 2. The Bernoulli Problem.- 2.1 The Physical Concept of Probability.- 2.2 Distribution Laws for Random Variables.- 2.3 The Binomial Distribution Law.- 2.4 Examples of Applications of the Binomial Law.- 2.5 Shot Effect. The Poisson Distribution.- 2.6 The De Moivre-Laplace Limit Theorem.- 2.7 Normal or Gaussian Distribution Law.- 2.8 Exercises.- 3. Random Pulses.- 3.1 Statement of the Problem.- 3.2 Characteristic Functions.- 3.3 Distribution Function for a Poisson Pulse Process.- 3.4 Covariance.- 3.5 Some Generalization of the Pulse Problem.- 3.6 Impulse Noise and the Central Limit Theorem.- 3.7 Exercises.- 4. Random Functions.- 4.1 General Definitions.- 4.2 Markov Processes.- 4.3 Stationary Processes.- 4.4 Moments of Random Functions.- 4.5 Correlation Theory.- 4.6 Probabilistic Convergence.- 4.7 Ergodicity of Random Processes.- 4.8 Exercises.- 5. Markov Processes.- 5.1 Preliminary Remarks.- 5.2 Smoluchowski Equation.- 5.3 Markov Process with Discrete States.- 5.4 Transition from Discrete Sequence to Processes with Continuous Sets of States Rayleigh Distribution.- 5.5 Some Generalizations of the Rayleigh Distribution.- 5.6 Continuous Markov Processes. The Einstein-Fokker-Planck Equation.- 5.7 Generalization to Multivariate Random Functions.- 5.8 Fluctuations in the Thomson Vacuum-Tube Oscillator.- 5.9 Fluctuations at Large Self-Oscillation Amplitudes.- 5.10 Rotational Brownian Motion. Random Refraction of a Ray.- 5.11 Stepwise Markov Processes. The Kolmogorov-Feller Equation.- 5.12 First Passage Problem.- 5.13 Exercises.- 6. Stochastic Differential Equations.- 6.1 Statement of the Problem.- 6.2 Random Functions with Independent Increments.- 6.3 Simple Example of a Stochastic Differential Equation.- 6.4 General Case of First-Order Equations and a Set of Such Equations for Gaussian Delta-Correlated Action.- 6.5 Stochastic Equation for Random Actions with Arbitrary Distribution Laws.- 6.6 Exercises.- References.