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 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 Prasanna Sahoo - University of Louisville
This book is an introduction to probability and mathematical statistics intended for students already having some elementary mathematical background. It is intended for a one-year junior or senior level undergraduate or beginning graduate course.
by O. Melchert - arXiv
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).
by Matthias Vallentin
The cookbook contains a succinct representation of various topics in probability theory and statistics. It provides a comprehensive reference reduced to the mathematical essence, rather than aiming for elaborate explanations.