Martingale Approximation
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Martingale Approximation
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Author : Yu. V. Borovskikh
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-01-14
Martingale Approximation written by Yu. V. Borovskikh and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-14 with Mathematics categories.
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Fluctuations In Markov Processes
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Author : Tomasz Komorowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-05
Fluctuations In Markov Processes written by Tomasz Komorowski 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 2012-07-05 with Mathematics categories.
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Martingale Limit Theory And Its Application
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Author : P. Hall
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Martingale Limit Theory And Its Application written by P. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
On The Martingale Representation Theorem And Approximate Hedging A Contingent Claim In The Minimum Mean Square Deviation Criterion
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Author :
language : en
Publisher: Dr. Vuong Quan Hoang
Release Date :
On The Martingale Representation Theorem And Approximate Hedging A Contingent Claim In The Minimum Mean Square Deviation Criterion written by and has been published by Dr. Vuong Quan Hoang this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A Proposition On The Martingale Representation Theorem And On The Approximate Hedging Of Contingent Claim In Mean Variance Criterion
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Author :
language : en
Publisher: Dr. Vuong Quan Hoang
Release Date :
A Proposition On The Martingale Representation Theorem And On The Approximate Hedging Of Contingent Claim In Mean Variance Criterion written by and has been published by Dr. Vuong Quan Hoang this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Approximation Of The Basic Martingale
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Author : A. J. Koning
language : en
Publisher:
Release Date : 1991
Approximation Of The Basic Martingale written by A. J. Koning and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
A Martingale Approach For The Approximation Of The Size Of A Rumour
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Author : Paul Yip
language : en
Publisher:
Release Date : 1988
A Martingale Approach For The Approximation Of The Size Of A Rumour written by Paul Yip and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Martingales (Mathematics) categories.
Probability Approximations And Beyond
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Author : Andrew Barbour
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-07
Probability Approximations And Beyond written by Andrew Barbour 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 2011-12-07 with Mathematics categories.
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Asymptotic Laws And Methods In Stochastics
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Author : Donald Dawson
language : en
Publisher: Springer
Release Date : 2015-11-12
Asymptotic Laws And Methods In Stochastics written by Donald Dawson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-12 with Mathematics categories.
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Functional Gaussian Approximation For Dependent Structures
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Author : Florence Merlevède
language : en
Publisher: Oxford University Press
Release Date : 2019-02-14
Functional Gaussian Approximation For Dependent Structures written by Florence Merlevède and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.