Variants Of Random Walks

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Asymptotic Analysis Of Random Walks

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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2008

Asymptotic Analysis Of Random Walks written by Aleksandr Alekseevich Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Asymptotic expansions categories.

This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition.

Random Walk A Modern Introduction

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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24

Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.

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.

Elements Of The Random Walk

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Author : Joseph Rudnick
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-25

Elements Of The Random Walk written by Joseph Rudnick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-25 with Science categories.

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its self-contained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

Random Walks And Electric Networks

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Author : Peter G. Doyle
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31

Random Walks And Electric Networks written by Peter G. Doyle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Electric network topology categories.

Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

Random Walks On Infinite Graphs And Groups

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Author : Wolfgang Woess
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13

Random Walks On Infinite Graphs And Groups written by Wolfgang Woess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.

The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Variants Of Random Walks

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Author : Source Wikipedia
language : en
Publisher: Booksllc.Net
Release Date : 2013-09

Variants Of Random Walks written by Source Wikipedia and has been published by Booksllc.Net this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Branching random walk, Brownian motion, Gambler's ruin, Heterogeneous random walk in one dimension, Loop-erased random walk, Ornstein-Uhlenbeck process, Reflected Brownian motion, Wiener process. Excerpt: A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905. Random walks have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry, and biology. Random walks explain the observed behaviors of processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity. Various different types of random walks are of interest. Often, random walks are assumed to be Markov chains or Markov processes, but other, more complicated walks are also of interest. Some random walks are on graphs, others on the line, in the plane, or in higher dimensions, while some random walks are on groups. Random walks also vary with regard to the time parameter. Often, the walk is in discrete time, and indexed by the natural numbers, as in . However, some walks take their steps at random times, and in that case the position is defined for the continuum of times . Specific cases or limits of random walks include the Levy flight. Random walks are related to the diffusion models and are a fundamental topic in discussions of Markov processes. Several properties of random walks, including dispersal distributions, first-passage times and encounter rates, have been extensively studied. A popular random...

Stochastic Calculus For Finance Ii

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Author : Steven E. Shreve
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-03

Stochastic Calculus For Finance Ii written by Steven E. Shreve and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Business & Economics categories.

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Variational And Diffusion Problems In Random Walk Spaces

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Author : José M. Mazón
language : en
Publisher: Springer Nature
Release Date : 2023-08-04

Variational And Diffusion Problems In Random Walk Spaces written by José M. Mazón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-04 with Mathematics categories.

This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research. Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.

Random Walks And Geometry

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Author : Vadim A. Kaimanovich
language : en
Publisher: Walter de Gruyter
Release Date : 2004

Random Walks And Geometry written by Vadim A. Kaimanovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schrödinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others. The contributors to the volume are the leading experts in the area.

Limit Theorems For Functionals Of Random Walks

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Author : A. N. Borodin
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Limit Theorems For Functionals Of Random Walks written by A. N. Borodin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

This book examines traditional problems in the theory of random walks: limit theorems for additive and multiadditive functionals defined on a random walk. Although the problems are traditional, the methods presented here are new. The book is intended for experts in probability theory and its applications, as well as for undergraduate and graduate students specializing in these areas.