Download and Read Online Lectures On The Poisson Process Book

Download Lectures On The Poisson Process Book PDF, Read Online Lectures On The Poisson Process Book Epub. Ebook Lectures On The Poisson Process Tuebl Download Online. The following is a list of various book titles based on search results using the keyword lectures on the poisson process. Click "GET BOOK" on the book you want. Register now and create a free account to access unlimited books, fast download, ad-free and books in good quality!

Lectures on the Poisson Process

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

CLICK HERE TO GET BOOK

Book Lectures on the Poisson Process Description/Summary:

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Lectures on the Poisson Process

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Release : 2017-10-26
Category : Mathematics
ISBN : 9781108514903

CLICK HERE TO GET BOOK

Book Lectures on the Poisson Process Description/Summary:

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.

Poisson Line Cox Process

Author : Harpreet S. Dhillon,Vishnu Vardhan Chetlur
Publisher : Morgan & Claypool Publishers
Release : 2020-06-24
Category : Computers
ISBN : 9781681738437

CLICK HERE TO GET BOOK

Book Poisson Line Cox Process Description/Summary:

This book provides a comprehensive treatment of the Poisson line Cox process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a Poisson line process (PLP) as per an independent Poisson point process (PPP). For vehicular applications, one can imagine the layout of the road network as a PLP and the vehicles on the roads as the points of the PLCP. First, a brief historical account of the evolution of the theory of PLP is provided to familiarize readers with the seminal contributions in this area. In order to provide a self-contained treatment of this topic, the construction and key fundamental properties of both PLP and PLCP are discussed in detail. The rest of the book is devoted to the applications of these models to a variety of wireless networks, including vehicular communication networks and localization networks. Specifically, modeling the locations of vehicular nodes and roadside units (RSUs) using PLCP, the signal-to-interference-plus-noise ratio (SINR)-based coverage analysis is presented for both ad hoc and cellular network models. For a similar setting, the load on the cellular macro base stations (MBSs) and RSUs in a vehicular network is also characterized analytically. For the localization networks, PLP is used to model blockages, which is shown to facilitate the characterization of asymptotic blind spot probability in a localization application. Finally, the path distance characteristics for a special case of PLCP are analyzed, which can be leveraged to answer critical questions in the areas of transportation networks and urban planning. The book is concluded with concrete suggestions on future directions of research. Based largely on the original research of the authors, this is the first book that specifically focuses on the self-contained mathematical treatment of the PLCP. The ideal audience of this book is graduate students as well as researchers in academia and industry who are familiar with probability theory, have some exposure to point processes, and are interested in the field of stochastic geometry and vehicular networks. Given the diverse backgrounds of the potential readers, the focus has been on providing an accessible and pedagogical treatment of this topic by consciously avoiding the measure theoretic details without compromising mathematical rigor.

Discrete Stochastic Processes

Author : Robert G. Gallager
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461523291

CLICK HERE TO GET BOOK

Book Discrete Stochastic Processes Description/Summary:

Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Release : 2014-01-09
Category : Mathematics
ISBN : 9783642376320

CLICK HERE TO GET BOOK

Book Fluctuations of Lévy Processes with Applications Description/Summary:

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.

Combinatorial Stochastic Processes

Author : Jim Pitman
Publisher : Springer Science & Business Media
Release : 2006-05-11
Category : Mathematics
ISBN : 9783540309901

CLICK HERE TO GET BOOK

Book Combinatorial Stochastic Processes Description/Summary:

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Introduction to Probability

Author : Dimitri P. Bertsekas,John N. Tsitsiklis
Publisher : Unknown
Release : 2002
Category : Mathematics
ISBN : UOM:39015066809040

CLICK HERE TO GET BOOK

Book Introduction to Probability Description/Summary:

Lectures on Risk Theory

Author : Anonim
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783322905703

CLICK HERE TO GET BOOK

Book Lectures on Risk Theory Description/Summary:

Twenty-five years ago, Hans Blihlmann published his famous monograph Mathe matical Methods in Risk Theory in the series Grundlehren der Mathematischen Wis8enschaften and thus established nonlife actuarial mathematics as a recognized subject of probability theory and statistics with a glance towards economics. This book was my guide to the subject when I gave my first course on nonlife actuarial mathematics in Summer 1988, but at the same time I tried to incorporate into my lectures parts of the rapidly growing literature in this area which to a large extent was inspired by Blihlmann's book. The present book is entirely devoted to a single topic of risk theory: Its subject is the development in time of a fixed portfolio of risks. The book thus concentrates on the claim number process and its relatives, the claim arrival process, the aggregate claims process, the risk process, and the reserve process. Particular emphasis is laid on characterizations of various classes of claim number processes, which provide alternative criteria for model selection, and on their relation to the trinity of the binomial, Poisson, and negativebinomial distributions. Special attention is also paid to the mixed Poisson process, which is a useful model in many applications, to the problems of thinning, decomposition, and superposition of risk processe8, which are important with regard to reinsurance, and to the role of martingales, which occur in a natural way in canonical situations.

Poisson Processes

Author : J. F. C. Kingman
Publisher : Clarendon Press
Release : 1992-12-17
Category : Mathematics
ISBN : 9780191591242

CLICK HERE TO GET BOOK

Book Poisson Processes Description/Summary:

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.

Lectures on the Coupling Method

Author : Torgny Lindvall
Publisher : Courier Corporation
Release : 2012-08-15
Category : Mathematics
ISBN : 9780486153247

CLICK HERE TO GET BOOK

Book Lectures on the Coupling Method Description/Summary:

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.

Stochastic Analysis for Poisson Point Processes

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319052335

CLICK HERE TO GET BOOK

Book Stochastic Analysis for Poisson Point Processes Description/Summary:

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Lectures in Elementary Probability Theory and Stochastic Processes

Author : Jean-Claude Falmagne
Publisher : McGraw-Hill Science, Engineering & Mathematics
Release : 2002
Category : Mathematics
ISBN : UOM:39015055088333

CLICK HERE TO GET BOOK

Book Lectures in Elementary Probability Theory and Stochastic Processes Description/Summary:

This text is designed for undergraduate mathematics students or graduate students in the sciences. Each chapter corresponds to a fifty-minute lecture. LECTURES IN ELEMENTARY PROBABILITY THEORY AND STOCHASTIC PROCESSES can be used in a prerequisite course for Statistics (for math majors) or Mathematical Modeling. The first eighteen chapters could be used in a one-quarter course, and the entire text is appropriate for a one-semester course.

Lectures on Random Voronoi Tessellations

Author : Jesper Moller
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226529

CLICK HERE TO GET BOOK

Book Lectures on Random Voronoi Tessellations Description/Summary:

Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.

Point Process Calculus in Time and Space

Author : Pierre Brémaud
Publisher : Springer Nature
Release : 2020-12-05
Category : Mathematics
ISBN : 9783030627539

CLICK HERE TO GET BOOK

Book Point Process Calculus in Time and Space Description/Summary:

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

Selected Topics in Malliavin Calculus

Author : Laurent Decreusefond
Publisher : Springer Nature
Release : 2022-06-23
Category : Mathematics
ISBN : 9783031013119

CLICK HERE TO GET BOOK

Book Selected Topics in Malliavin Calculus Description/Summary:

This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all the results which are known even for the basic subjects which are addressed here. The goal was to give the largest possible variety of proof techniques. For instance, we did not focus on the proof of concentration inequality for functionals of the Brownian motion, as it closely follows the lines of the analog result for Poisson functionals. This book grew from the graduate courses I gave at Paris-Sorbonne and Paris-Saclay universities, during the last few years. It is supposed to be as accessible as possible for students who have knowledge of Itô calculus and some rudiments of functional analysis.

Introductory Lectures on Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Release : 2006-12-18
Category : Mathematics
ISBN : 9783540313434

CLICK HERE TO GET BOOK

Book Introductory Lectures on Fluctuations of Lévy Processes with Applications Description/Summary:

This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.

Elementary Lectures in Statistical Mechanics

Author : George D.J. Phillies
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Science
ISBN : 9781461212645

CLICK HERE TO GET BOOK

Book Elementary Lectures in Statistical Mechanics Description/Summary:

This textbook for graduates and advanced undergraduates in physics and physical chemistry covers the major areas of statistical mechanics and concludes with the level of current research. It begins with the fundamental ideas of averages and ensembles, focusing on classical systems described by continuous variables such as position and momentum, and using the ideal gas as an example. It then turns to quantum systems, beginning with diatomic molecules and working up through blackbody radiation and chemical equilibria. The discussion of equilibrium properties of systems of interacting particles includes such techniques as cluster expansions and distribution functions and uses non-ideal gases, liquids, and solutions. Dynamic behavior -- treated here more extensively than in other texts -- is discussed from the point of view of correlation functions. The text concludes with the problem of diffusion in a suspension of interacting hard spheres and what can be learned about such a system from scattered light. Intended for a one-semester course, the text includes several "asides" on topics usually omitted from introductory courses, as well as numerous exercises.

Power Laws

Author : Iddo Eliazar
Publisher : Springer Nature
Release : 2020-01-03
Category : Science
ISBN : 9783030332358

CLICK HERE TO GET BOOK

Book Power Laws Description/Summary:

This monograph is a comprehensive and cohesive exposition of power-law statistics. Following a bottom-up construction from a foundational bedrock – the power Poisson process – this monograph presents a unified study of an assortment of power-law statistics including: Pareto laws, Zipf laws, Weibull and Fréchet laws, power Lorenz curves, Lévy laws, power Newcomb-Benford laws, sub-diffusion and super-diffusion, and 1/f and flicker noises. The bedrock power Poisson process, as well as the assortment of power-law statistics, are investigated via diverse perspectives: structural, stochastic, fractal, dynamical, and socioeconomic. This monograph is poised to serve researchers and practitioners – from various fields of science and engineering – that are engaged in analyses of power-law statistics.

Poisson Point Processes and Their Application to Markov Processes

Author : Kiyosi Itô
Publisher : Springer
Release : 2015-12-24
Category : Mathematics
ISBN : 9789811002724

CLICK HERE TO GET BOOK

Book Poisson Point Processes and Their Application to Markov Processes Description/Summary:

An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m