| Introduction | p. ix |
| Stochastic Processes | p. 1 |
| Introduction | p. 1 |
| Foundations of Probability | p. 1 |
| Intuitive Definition of Probability | p. 3 |
| Random Variables | p. 11 |
| Stochastic Processes | p. 15 |
| Probability Distribution and Probability Density | p. 19 |
| Expectation and Conditional Mathematical Expectation | p. 23 |
| Characteristic Function | p. 35 |
| Orthogonal and Uncorrelated Sequences | p. 37 |
| On Convergence | p. 41 |
| Finite Markov Chains | p. 46 |
| Renewal Processes | p. 62 |
| Martingale, Supermartingale, Submartingale | p. 68 |
| Examples of Martingales | p. 69 |
| Martingale Convergence Theorems | p. 80 |
| Some Definitions | p. 84 |
| Conclusions | p. 88 |
| Estimation of Probability Densities | p. 93 |
| Introduction | p. 93 |
| Main Probability Distributions | p. 93 |
| Bernoulli Distribution | p. 94 |
| Binomial Distribution | p. 94 |
| Hypergeometric Distribution | p. 95 |
| Poisson Distribution | p. 96 |
| Gaussian Distribution | p. 99 |
| Truncated Normal Distribution | p. 102 |
| Lognormal Distribution | p. 102 |
| Laplace Distribution | p. 104 |
| Cauchy Distribution | p. 105 |
| Exponential Distribution | p. 106 |
| Geometric Distribution | p. 108 |
| Rayleigh Distribution | p. 109 |
| Gamma Distribution | p. 110 |
| Weibull Distribution | p. 111 |
| Skewness and Kurtosis Measures | p. 117 |
| Classification of Probability Distributions | p. 121 |
| Transformation of Random Variables | p. 123 |
| Estimation of Probability Density Functions | p. 130 |
| Method of Moments | p. 131 |
| Series of Rectangular Pulses | p. 132 |
| Modeling Using Polynomials | p. 133 |
| Kernel Estimators | p. 134 |
| Maximum Likelihood | p. 136 |
| Expectation Maximization | p. 138 |
| Neural Networks | p. 141 |
| Numerical Examples | p. 146 |
| EM algorithm | p. 146 |
| Kurtosis-based EM-algorithm | p. 147 |
| Maximum Likelihood Estimation Using SNN | p. 149 |
| Model Validation | p. 153 |
| The x[superscript 2] Approach | p. 153 |
| Kolmogorov Criterion | p. 156 |
| Stochastic Approximation | p. 157 |
| Conclusion | p. 160 |
| Optimization Techniques | p. 167 |
| Introduction | p. 167 |
| Stochastic Approximation Techniques | p. 168 |
| Unconstrained Optimization Using Gradient Measurements | p. 168 |
| Unconstrained Optimization Using Function Measurements | p. 170 |
| Optimization under Constraints | p. 171 |
| Learning Automata | p. 173 |
| Learning Automaton | p. 173 |
| Unconstrained Optimization | p. 177 |
| Optimization under Constraints | p. 183 |
| Applications of Learning Automata | p. 188 |
| Simulated Annealing | p. 211 |
| Genetic Algorithms | p. 214 |
| Conclusions | p. 216 |
| Analysis of Recursive Algorithms | p. 223 |
| Introduction | p. 223 |
| The Analysis of Recursive Algorithms | p. 224 |
| Vector Form | p. 224 |
| Lyapunov Approach | p. 226 |
| Robbins-Monro Approach | p. 229 |
| The Ordinary Differential Equation | p. 232 |
| Summary | p. 233 |
| Use of Some Inequalities, Lemmas and Theorems | p. 234 |
| Case 1: Single Learning Automaton | p. 254 |
| Learning Automata | p. 255 |
| Projection Procedure | p. 256 |
| Stochastic Learning Model | p. 257 |
| Asymptotic Properties | p. 260 |
| Numerical Example | p. 263 |
| Conclusions | p. 269 |
| Case 2: Team of Binary Learning Automata | p. 269 |
| Stochastic Learning Automata | p. 271 |
| Optimization Algorithm | p. 272 |
| Asymptotic Properties | p. 279 |
| Numerical Example | p. 285 |
| Conclusions | p. 287 |
| Convergence Rate | p. 288 |
| Convergence with Probability 1 | p. 290 |
| Normalized Deviation | p. 293 |
| Rate of Mean Squares Convergence | p. 295 |
| Asymptotic Normality and Rate of Convergence in Distribution Sense | p. 296 |
| Rate of Almost Sure Convergence | p. 298 |
| Optimization of the Convergence Rate on the Basis of the Gain Matrix Selection | p. 298 |
| Feasible Realization of the Optimal Gain Matrix | p. 301 |
| Summary | p. 305 |
| Inequalities, Lemmas and Theorems | p. 315 |
| Inequalities | p. 315 |
| Lemmas | p. 320 |
| Theorems | p. 323 |
| Matlab Program | p. 327 |
| Index | p. 329 |
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