Probability with Martingales
Title | Probability with Martingales PDF eBook |
Author | David Williams |
Publisher | Cambridge University Press |
Pages | 274 |
Release | 1991-02-14 |
Genre | Mathematics |
ISBN | 9780521406055 |
This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.
Martingale Limit Theory and Its Application
Title | Martingale Limit Theory and Its Application PDF eBook |
Author | P. Hall |
Publisher | Academic Press |
Pages | 321 |
Release | 2014-07-10 |
Genre | Mathematics |
ISBN | 1483263223 |
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Measures, Integrals and Martingales
Title | Measures, Integrals and Martingales PDF eBook |
Author | René L. Schilling |
Publisher | Cambridge University Press |
Pages | 404 |
Release | 2005-11-10 |
Genre | Mathematics |
ISBN | 9780521850155 |
This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.
Probability
Title | Probability PDF eBook |
Author | Rick Durrett |
Publisher | Cambridge University Press |
Pages | |
Release | 2010-08-30 |
Genre | Mathematics |
ISBN | 113949113X |
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Probability Theory
Title | Probability Theory PDF eBook |
Author | Achim Klenke |
Publisher | Springer Science & Business Media |
Pages | 621 |
Release | 2007-12-31 |
Genre | Mathematics |
ISBN | 1848000480 |
Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.
Probability Essentials
Title | Probability Essentials PDF eBook |
Author | Jean Jacod |
Publisher | Springer Science & Business Media |
Pages | 247 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642556825 |
This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.
A Modern Approach to Probability Theory
Title | A Modern Approach to Probability Theory PDF eBook |
Author | Bert E. Fristedt |
Publisher | Springer Science & Business Media |
Pages | 775 |
Release | 2013-11-21 |
Genre | Mathematics |
ISBN | 1489928375 |
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.