Lectures on the Poisson Process - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Poisson Process write by Günter Last. This book was released on 2017-10-26. Lectures on the Poisson Process available in PDF, EPUB and Kindle. A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Lectures on the Poisson Process
Lectures on the Poisson Process - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Poisson Process write by Günter Last. This book was released on 2017-10-26. Lectures on the Poisson Process available in PDF, EPUB and Kindle. The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.
Lectures on the Coupling Method
Lectures on the Coupling Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Coupling Method write by Torgny Lindvall. This book was released on 2012-08-15. Lectures on the Coupling Method available in PDF, EPUB and Kindle. Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
An Introduction to Stein's Method
An Introduction to Stein's Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Stein's Method write by A. D. Barbour. This book was released on 2005. An Introduction to Stein's Method available in PDF, EPUB and Kindle. A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Poisson Processes
Poisson Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poisson Processes write by J. F. C. Kingman. This book was released on 1992-12-17. Poisson Processes available in PDF, EPUB and Kindle. In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.
