Normal Approximations with Malliavin Calculus
Title | Normal Approximations with Malliavin Calculus PDF eBook |
Author | Ivan Nourdin |
Publisher | |
Pages | 256 |
Release | 2014-05-14 |
Genre | MATHEMATICS |
ISBN | 9781139380218 |
"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"--
Normal Approximations with Malliavin Calculus
Title | Normal Approximations with Malliavin Calculus PDF eBook |
Author | Ivan Nourdin |
Publisher | Cambridge University Press |
Pages | 255 |
Release | 2012-05-10 |
Genre | Mathematics |
ISBN | 1107017777 |
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Malliavin Calculus and Normal Approximations
Title | Malliavin Calculus and Normal Approximations PDF eBook |
Author | David Nualart |
Publisher | |
Pages | 0 |
Release | 2019 |
Genre | |
ISBN |
Normal Approximation by Stein’s Method
Title | Normal Approximation by Stein’s Method PDF eBook |
Author | Louis H.Y. Chen |
Publisher | Springer Science & Business Media |
Pages | 411 |
Release | 2010-10-13 |
Genre | Mathematics |
ISBN | 3642150071 |
Since 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.
Introduction to Malliavin Calculus
Title | Introduction to Malliavin Calculus PDF eBook |
Author | David Nualart |
Publisher | Cambridge University Press |
Pages | 249 |
Release | 2018-09-27 |
Genre | Business & Economics |
ISBN | 1107039126 |
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Malliavin Calculus and Normal Approximations ; And, Spatial Population Models
Title | Malliavin Calculus and Normal Approximations ; And, Spatial Population Models PDF eBook |
Author | David Nualart |
Publisher | |
Pages | |
Release | 2019 |
Genre | |
ISBN | 9788583371649 |
Selected Aspects of Fractional Brownian Motion
Title | Selected Aspects of Fractional Brownian Motion PDF eBook |
Author | Ivan Nourdin |
Publisher | Springer Science & Business Media |
Pages | 133 |
Release | 2013-01-17 |
Genre | Mathematics |
ISBN | 884702823X |
Fractional 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.