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Author: Ivan Nourdin
Publisher: Cambridge University Press
Published: 2012-05-10
Total Pages: 255
ISBN-13: 1107017777
DOWNLOAD EBOOKThis book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Author: David Nualart
Publisher: Cambridge University Press
Published: 2018-09-27
Total Pages: 249
ISBN-13: 1107039126
DOWNLOAD EBOOKA compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Author: Louis H.Y. Chen
Publisher: Springer Science & Business Media
Published: 2010-10-13
Total Pages: 411
ISBN-13: 3642150071
DOWNLOAD EBOOKSince its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Author: Ivan Nourdin
Publisher: Springer Science & Business Media
Published: 2013-01-17
Total Pages: 133
ISBN-13: 884702823X
DOWNLOAD EBOOKFractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.
Author: Hiroyuki Matsumoto
Publisher: Cambridge University Press
Published: 2017
Total Pages: 359
ISBN-13: 110714051X
DOWNLOAD EBOOKDeveloping the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.
Author: A. D. Barbour
Publisher: World Scientific
Published: 2005
Total Pages: 240
ISBN-13: 981256280X
DOWNLOAD EBOOKA common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Author: Ivan Nourdin
Publisher:
Published: 2014-05-14
Total Pages: 256
ISBN-13: 9781139380218
DOWNLOAD EBOOK"This is a text about probabilistic approximations, which are mathematical statements providing estimates of the distance between the laws of two random objects. As the title suggests, we will be mainly interested in approximations involving one or more normal (equivalently called Gaussian) random elements. Normal approximations are naturally connected with central limit theorems (CLTs), i.e. convergence results displaying a Gaussian limit, and are one of the leading themes of the whole theory of probability"--
Author: Vladimir Igorevich Bogachev
Publisher: American Mathematical Soc.
Published: 2010-07-21
Total Pages: 506
ISBN-13: 082184993X
DOWNLOAD EBOOKThis book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Author: Horst Osswald
Publisher: Cambridge University Press
Published: 2012-03
Total Pages: 429
ISBN-13: 1107016142
DOWNLOAD EBOOKAfter functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Author: Rabi N. Bhattacharya
Publisher: SIAM
Published: 2010-11-11
Total Pages: 333
ISBN-13: 089871897X
DOWNLOAD EBOOK-Fourier analysis, --
