1. Stochastic processes -- Foundations of probability -- Finite Markov chains -- Renewal processes -- Martingale, supermartingale, submartingale -- 2. Estimation of probability densities -- Main probability distributions -- Skewness and Kurtosis measures -- Classification of probability distributions -- Transformation of random variables -- Estimation of probability density functions -- Numerical examples -- Model validation -- Stochastic approximation -- 3. Optimization techniques -- Stochastic approximation techniques -- Learning automata -- Simulated annealing -- Genetic algorithms -- 4. Analysis of recursive algorithms -- The analysis of recursive algorithms -- Use of some inequalities, lemmas and theorems -- Case 1 : single learning automaton -- Case 2 : team of binary learning automata -- Convergence rate -- App. A. Inequalities, lemmas and theorems -- App. B. Matlab program
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"A 'stochastic' process is a 'random' or 'conjectural' process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance." "The aim of this publication is to present important current tools used in the stochastic processes - estimation, optimization and recursive logarithms - in a form accessible to engineers (and that can also be applied to Matlab programs), and to gather together, in a unified presentation, many of the results in probability and statistics."--Jacket