Asymptotic Laws And Methods In Stochastics
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Author | : Donald Dawson |
Publisher | : Springer |
Total Pages | : 401 |
Release | : 2015-11-12 |
Genre | : Mathematics |
ISBN | : 1493930761 |
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.
Author | : M. Csörgö |
Publisher | : American Mathematical Soc. |
Total Pages | : 546 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835610 |
Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.
Author | : Dariusz Buraczewski |
Publisher | : Springer |
Total Pages | : 325 |
Release | : 2016-07-04 |
Genre | : Mathematics |
ISBN | : 3319296795 |
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.
Author | : D. Kannan |
Publisher | : CRC Press |
Total Pages | : 800 |
Release | : 2001-10-23 |
Genre | : Mathematics |
ISBN | : 9780824706609 |
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Author | : Nicolas Bouleau |
Publisher | : John Wiley & Sons |
Total Pages | : 402 |
Release | : 1994-01-14 |
Genre | : Mathematics |
ISBN | : 9780471546412 |
Gives greater rigor to numerical treatments of stochastic models. Contains Monte Carlo and quasi-Monte Carlo techniques, simulation of major stochastic procedures, deterministic methods adapted to Markovian problems and special problems related to stochastic integral and differential equations. Simulation methods are given throughout the text as well as numerous exercises.
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author | : Mathieu Kessler |
Publisher | : CRC Press |
Total Pages | : 509 |
Release | : 2012-05-17 |
Genre | : Mathematics |
ISBN | : 1439849404 |
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.
Author | : Johan Grasman |
Publisher | : Springer Science & Business Media |
Total Pages | : 242 |
Release | : 1999-03-08 |
Genre | : Mathematics |
ISBN | : 9783540644354 |
Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Author | : B. Szyszkowicz |
Publisher | : Elsevier |
Total Pages | : 925 |
Release | : 1998-10-29 |
Genre | : Mathematics |
ISBN | : 008049952X |
One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.
Author | : Zhongqiang Zhang |
Publisher | : Springer |
Total Pages | : 391 |
Release | : 2017-09-01 |
Genre | : Mathematics |
ISBN | : 3319575112 |
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.