Markov Chains and Stochastic Stability
by S.P. Meyn, R.L. Tweedie
Publisher: Springer 2005
Number of pages: 567
This book describes the modern theory of general state space Markov chains, and the application of that theory to operations research, time series analysis, and systems and control theory. It is intended as an advanced graduate text in any of these areas, as well as being a research monograph incorporating a new and thorough treatment of the stability of general Markov chains. Many of the theoretical results appear here for the first time, and much of the theory and the models which are used to illustrate the theory, and to provide extensions of the theory in special cases, have not previously been brought together in book form. This book thus provides a readable account of the development over the last two decades of a fundamental and applicable area of stochastic processes, and as such will be of value not only in probability theory but in the many discplines where these models form the basis of analysis.
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by Klaus Bichteler - University of Texas
Written for graduate students of mathematics, physics, electrical engineering, and finance. The students are expected to know the basics of point set topology up to Tychonoff's theorem, general integration theory, and some functional analysis.
by Alexander K. Hartmann - arXiv
This is a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous random variables.
by Luc Devroye - Springer
The book on small field on the crossroads of statistics, operations research and computer science. The applications of random number generators are wide and varied. The study of non-uniform random variates is precisely the subject area of the book.
by Cappella Archive - Prasenjit Saha
This is a short book about the principles of data analysis. The emphasis is on why things are done rather than on exactly how to do them. If you already know something about the subject, then working through this book will deepen your understanding.