Stochastic Modelling and Applied Probability: Random Iterative Models (PDF)

Be they random or non-random, iterative methods have progressively gained sway with the development of computer science and automatic control theory. Thus, being easy to conceive and simulate, stochastic processes defined by an iterative formula (linear or functional) have been the subject of many studies. The iterative structure often leads to simpler and more explicit arguments than certain classical theories of processes. On the other hand, when it comes to choosing step-by-step decision algorithms (sequential statistics, control, learning, ... ) recursive decision methods are indispensable. They lend themselves naturally to problems of the identification and control of iterative stochastic processes. In recent years, know-how in this area has advanced greatly; this is reflected in the corresponding theoretical problems, many of which remain open. At Whom Is This Book Aimed? I thought it useful to present the basic ideas and tools relating to random iterative models in a form accessible to a mathematician familiar with the classical concepts of probability and statistics but lacking experience in automatic control theory. Thus, the first aim of this book is to show young research workers that work in this area is varied and interesting and to facilitate their initiation period. The second aim is to present more seasoned probabilists with a number of recent original techniques and arguments relating to iterative methods in a fairly classical environment.