# Stochastic Processes

## Estimation, Optimisation and Analysis

A âstochasticâ process is a ârandomâ or âconjecturalâ 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.This book deals with the tools and techniques used in the stochastic process â estimation, optimisation and recursive logarithms â in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.

Audience
Students and practitioners in statistics, applied mathematics, automatic control, mechanical and electrical engineering, and those with special interests in topics such as insurance calculations that arise in engineering projects

Hardbound, 305 Pages

Published: July 2004

Imprint: Butterworth Heinemann

ISBN: 978-1-903996-55-3

## Contents

• 1. Stochastic Processes: Foundations of probability; Finite Markov chains; Renewal processes; Martingale, supermartingale, submartingale2. Probability Densities Estimation: Skewness and kurtosis measures; Transformation of random variables; Estimation of the probability density functions; Model validation; Numerical examples3. Optimisation Techniques: Stochastic approximation techniques; Learning automata; Simulated annealing; Genetic algorithms4. Analysis of Recursive Stochastic Algorithms: The analysis of recursive algorithms; Direct use of some inequalities, lemmas and theorems; Case 1 Learning automaton for global optimisation; Case 2 Optimisation based on a team learning automata with binary outputsAppendix A: Inequalities, lemmas and theoremsAppendix B: Matlab programs