Functional Limit Theorems For Non Stationary Stochastic Systems
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Functional Limit Theorems For Non Stationary Stochastic Systems
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Author : Yuhang Zhou
language : en
Publisher:
Release Date : 2018
Functional Limit Theorems For Non Stationary Stochastic Systems written by Yuhang Zhou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Modern service systems, such as call centers and health care systems, are typically of large scale and have non-stationary data, including customer arrival rates, service times and staffing. A better understanding of such service systems will help improving system efficiency, optimizing system managements, and reducing costs. However, exact analysis is hard because of the non-stationarity, randomness and large-scale of such systems. Stochastic models in the heavy-traffic regime turn out to be useful to obtain approximations and provide insights for operational managements. My primary work in this dissertation is to study stochastic models with non-stationarity and to establish associated functional limit theorems.I have established a novel and powerful framework for proving functional limit theorems for two-parameter processes describing the system dynamics of non-stationary non-Markovian queueing models. In particular, I have studied i) infinite- server queues with non-stationary arrival and service times (arrival dependent services), ii) infinite-server queues with non-stationary arrival and weakly dependent general service times, and iii) non-Markovian many-server queues with non-stationary arrival and service times.I have also studied a new class of non-stationary shot noise models where the distribution of each shot noise depends on the shot time. Shot noise processes have been extensively studied, and have many applications in physics, insurance risk theory, telecommunications, and service systems. In particular, they include the infinite-server queueing models as special cases. My work weakens the i.i.d. assumption on shot noises in the existing literature and thus provides more flexibilities for modeling non-stationary shot noise phenomena.Non-stationary stochastic models usually suffer from mathematical intractability. The main theoretical difficulty is the lack of appropriate maximal inequalities for general stochastic processes. I have developed maximal inequalities for two-parameter stochastic processes via the chaining method. In addition, sample path properties for Gaussian processes and classical criteria for weak convergence of stochastic processes have been generalized to broader settings.
Limit Theorems For Associated Random Fields And Related Systems
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Author : Aleksandr Vadimovich Bulinski?
language : en
Publisher: World Scientific
Release Date : 2007
Limit Theorems For Associated Random Fields And Related Systems written by Aleksandr Vadimovich Bulinski? and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
The Functional Central Limit Theorem For Non Stationary Mixing Sequences Of Random Variables
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Author : Geoffrey Roderick Webb
language : en
Publisher:
Release Date : 1971
The Functional Central Limit Theorem For Non Stationary Mixing Sequences Of Random Variables written by Geoffrey Roderick Webb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Distribution (Probability theory) categories.
Multiple Wiener Ito Integrals
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Author : P. Major
language : en
Publisher: Springer
Release Date : 2006-11-14
Multiple Wiener Ito Integrals written by P. Major and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Local Limit Theorems For Inhomogeneous Markov Chains
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Author : Dmitry Dolgopyat
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Local Limit Theorems For Inhomogeneous Markov Chains written by Dmitry Dolgopyat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Functional Limit Theorems For Stochastic Processes Based On Embedded Processes
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Author : Richard F. Serfozo
language : en
Publisher:
Release Date : 1974
Functional Limit Theorems For Stochastic Processes Based On Embedded Processes written by Richard F. Serfozo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Stochastic processes categories.
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory
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Author : Harold Joseph Kushner
language : en
Publisher: MIT Press
Release Date : 1984
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory written by Harold Joseph Kushner and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Computers categories.
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.
Limit Theorems For Large Deviations
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Author : L. Saulis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Limit Theorems For Large Deviations written by L. Saulis 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 2012-12-06 with Mathematics categories.
"Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series
Functional Weak Limit Theorem For A Local Empirical Process Of Non Stationary Time Series And Its Application To Von Mises Statistics
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Author : Ulrike Mayer
language : en
Publisher:
Release Date : 2019
Functional Weak Limit Theorem For A Local Empirical Process Of Non Stationary Time Series And Its Application To Von Mises Statistics written by Ulrike Mayer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Multiple Wiener It Integrals
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Author : Péter Major
language : en
Publisher: Springer
Release Date : 2013-12-02
Multiple Wiener It Integrals written by Péter Major and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Mathematics categories.
The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener–Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revised version of a previous volume written with the goal of giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments.