A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.
The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and...

This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0...

This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an...

The book will appeal to mathematicians working in probability theory, ergodic theory and number theory

The aim of" the present monograph is two-fold: (a) to give a short account of the main results concerning the theory of random systems with complete connections, and (b) to describe the general learning model by means of random systems with complete connections. The notion of chain with complete connections has been introduced in probability theory by ONICESCU and MIHOC (1935a). These authors have set themselves the aim to define a very broad type of dependence which takes into account the whole history of the evolution and thus includes as a special case the Markovian one. In a sequel of...

This volume is a revised and enlarged version of Chapters 1 and 2 of a book with the same title, published in Romanian in 1968. The revision resulted in a new book which has been divided into two parts because of the large amount of new material. The present part is intended to introduce mathematicians and biologists with a strong mathematical and probabilistic background to the study of stochastic processes. We hope some readers will be able to discover by themselves the new features of our treatment such as the inclusion of some unusual topics, the special attention paid to some usual...

This volume is a revised and enlarged version of Chapter 3 of. a book with the same title, published in Romanian in 1968. The revision resulted in a new book which has been divided into two of the large amount of new material. The whole book parts because is intended to introduce mathematicians and biologists with a strong mathematical background to the study of stochastic processes and their applications in biological sciences. It is meant to serve both as a textbook and a survey of recent developments. Biology studies complex situations and therefore needs skilful methods of abstraction....