Branching Random Walks
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Author |
: Zhan Shi |
Publisher |
: Springer |
Total Pages |
: 143 |
Release |
: 2016-02-04 |
ISBN-10 |
: 9783319253725 |
ISBN-13 |
: 3319253727 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Branching Random Walks by : Zhan Shi
Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.
Author |
: Jim Pitman |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 257 |
Release |
: 2006-05-11 |
ISBN-10 |
: 9783540309901 |
ISBN-13 |
: 354030990X |
Rating |
: 4/5 (01 Downloads) |
Synopsis Combinatorial Stochastic Processes by : Jim Pitman
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.
Author |
: Vladimir V. Rykov |
Publisher |
: Springer |
Total Pages |
: 551 |
Release |
: 2017-12-21 |
ISBN-10 |
: 9783319715049 |
ISBN-13 |
: 3319715046 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Analytical and Computational Methods in Probability Theory by : Vladimir V. Rykov
This book constitutes the refereed proceedings of the First International Conference on Analytical and Computational Methods in Probability Theory and its Applications, ACMPT 2017, held in Moscow, Russia, in October 2017. The 42 full papers presented were carefully reviewed and selected from 173 submissions. The conference program consisted of four main themes associated with significant contributions made by A.D.Soloviev. These are: Analytical methods in probability theory, Computational methods in probability theory, Asymptotical methods in probability theory, the history of mathematics.
Author |
: Russell Lyons |
Publisher |
: Cambridge University Press |
Total Pages |
: 1023 |
Release |
: 2017-01-20 |
ISBN-10 |
: 9781316785331 |
ISBN-13 |
: 1316785335 |
Rating |
: 4/5 (31 Downloads) |
Synopsis Probability on Trees and Networks by : Russell Lyons
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
Author |
: A. A. Borovkov |
Publisher |
: Cambridge University Press |
Total Pages |
: 437 |
Release |
: 2020-10-29 |
ISBN-10 |
: 9781108901208 |
ISBN-13 |
: 1108901204 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Asymptotic Analysis of Random Walks by : A. A. Borovkov
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Author |
: Pal Revesz |
Publisher |
: World Scientific |
Total Pages |
: 208 |
Release |
: 1994-09-12 |
ISBN-10 |
: 9789814501958 |
ISBN-13 |
: 9814501956 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Random Walks Of Infinitely Many Particles by : Pal Revesz
The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes.
Author |
: Gregory F. Lawler |
Publisher |
: Cambridge University Press |
Total Pages |
: 376 |
Release |
: 2010-06-24 |
ISBN-10 |
: 0521519187 |
ISBN-13 |
: 9780521519182 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Random Walk: A Modern Introduction by : Gregory F. Lawler
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Author |
: Rabi Bhattacharya |
Publisher |
: Springer Nature |
Total Pages |
: 396 |
Release |
: 2021-09-20 |
ISBN-10 |
: 9783030789398 |
ISBN-13 |
: 303078939X |
Rating |
: 4/5 (98 Downloads) |
Synopsis Random Walk, Brownian Motion, and Martingales by : Rabi Bhattacharya
This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.
Author |
: J. T. Cox |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 114 |
Release |
: 2004 |
ISBN-10 |
: 9780821835425 |
ISBN-13 |
: 0821835424 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis by : J. T. Cox
Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.
Author |
: Albert N. Shiryaev |
Publisher |
: Springer Nature |
Total Pages |
: 370 |
Release |
: 2021-08-02 |
ISBN-10 |
: 9783030832667 |
ISBN-13 |
: 303083266X |
Rating |
: 4/5 (67 Downloads) |
Synopsis Recent Developments in Stochastic Methods and Applications by : Albert N. Shiryaev
Highlighting the latest advances in stochastic analysis and its applications, this volume collects carefully selected and peer-reviewed papers from the 5th International Conference on Stochastic Methods (ICSM-5), held in Moscow, Russia, November 23-27, 2020. The contributions deal with diverse topics such as stochastic analysis, stochastic methods in computer science, analytical modeling, asymptotic methods and limit theorems, Markov processes, martingales, insurance and financial mathematics, queueing theory and stochastic networks, reliability theory, risk analysis, statistical methods and applications, machine learning and data analysis. The 29 articles in this volume are a representative sample of the 87 high-quality papers accepted and presented during the conference. The aim of the ICSM-5 conference is to promote the collaboration of researchers from Russia and all over the world, and to contribute to the development of the field of stochastic analysis and applications of stochastic models.