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Author: Yu. V. Borovskikh
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944685
Category : Mathematics
Languages : en
Pages : 336
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Book Description
No detailed description available for "Martingale Approximation".
Author: Yu. V. Borovskikh
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944685
Category : Mathematics
Languages : en
Pages : 336
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Book Description
No detailed description available for "Martingale Approximation".
Author: Tomasz Komorowski
Publisher: Springer Science & Business Media
ISBN: 364229880X
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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.
Author: Florence Merlevède
Publisher: Oxford University Press
ISBN: 0192561863
Category : Mathematics
Languages : en
Pages : 496
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Book Description
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.
Author:
Publisher: Dr. Vuong Quan Hoang
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
Author: Andrew Barbour
Publisher: Springer Science & Business Media
ISBN: 1461419654
Category : Mathematics
Languages : en
Pages : 166
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Book Description
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.
Author: Radosław Adamczak
Publisher: Springer Nature
ISBN: 3031269799
Category : Mathematics
Languages : en
Pages : 445
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Book Description
This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
Author: Peter H. Rossi
Publisher: Elsevier
ISBN: 0080511872
Category : Business & Economics
Languages : en
Pages : 505
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Book Description
This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing. Provides for the first time new insights on the links between continuous time and ARCH models Collects seminal scholarship by some of the most renowned researchers in finance and econometrics Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics
Author: Patrice Bertail
Publisher: Springer Science & Business Media
ISBN: 038736062X
Category : Mathematics
Languages : en
Pages : 491
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Book Description
This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.
Author: Yuliya Mishura
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110652994
Category : Mathematics
Languages : en
Pages : 222
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Book Description
The De Gruyter Series in Probability and Stochastics is devoted to the publication of high-level monographs and specialized graduate texts in any branch of modern probability theory and stochastics, along with their numerous applications in other parts of mathematics, physics and informatics, in economics and finance, and in the life sciences. The aim of the series is to present recent research results in the form of authoritative and comprehensive works that will serve the probability and stochastics community as basis for further research. Editorial Board Itai Benjamini, Weizmann Institute of Science, Israel Jean Bertoin, Universität Zürich, Switzerland Michel Ledoux, Université de Toulouse, France René L. Schilling, Technische Universität Dresden, Germany
Author: Harold Joseph Kushner
Publisher: MIT Press
ISBN: 9780262110907
Category : Computers
Languages : en
Pages : 296
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Book Description
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
