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Author: Olav Kallenberg Publisher: Springer ISBN: 3319415980 Category : Mathematics Languages : en Pages : 680
Book Description
Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Author: Olav Kallenberg Publisher: Springer ISBN: 3319415980 Category : Mathematics Languages : en Pages : 680
Book Description
Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Author: Olav Kallenberg Publisher: Springer Science & Business Media ISBN: 9780387953137 Category : Mathematics Languages : en Pages : 670
Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author: John Goutsias Publisher: Springer Science & Business Media ISBN: 1461219426 Category : Mathematics Languages : en Pages : 417
Book Description
This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.
Author: D.J. Daley Publisher: Springer Science & Business Media ISBN: 0387215646 Category : Mathematics Languages : en Pages : 471
Book Description
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Author: Rick Durrett Publisher: Cambridge University Press ISBN: 113949113X Category : Mathematics Languages : en Pages :
Book Description
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.
Author: Efe A. Ok Publisher: Princeton University Press ISBN: 1400840899 Category : Business & Economics Languages : en Pages : 832
Book Description
There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.
Author: Patrick Billingsley Publisher: SIAM ISBN: 9781611970623 Category : Mathematics Languages : en Pages : 37
Book Description
A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.
Author: Patrick Billingsley Publisher: John Wiley & Sons ISBN: 1118122372 Category : Mathematics Languages : en Pages : 660
Book Description
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including: An improved treatment of Brownian motion Replacement of queuing theory with ergodic theory Theory and applications used to illustrate real-life situations Over 300 problems with corresponding, intensive notes and solutions Updated bibliography An extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.
Author: Olav Kallenberg
Author: Olav Kallenberg
Author: Olav Kallenberg
Author: John Goutsias
Author: Ross Leadbetter
Author: D.J. Daley
Author: Rick Durrett
Author: Efe A. Ok
Author: G. Kallianpur
Author: Patrick Billingsley
Author: Patrick Billingsley