Download or read book Normal Approximations with Malliavin Calculus written by Ivan Nourdin and published by . This book was released on 2014-05-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
Download or read book Normal Approximations with Malliavin Calculus written by Ivan Nourdin and published by Cambridge University Press. This book was released on 2012-05-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Download or read book Malliavin Calculus and Normal Approximations written by David Nualart and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Normal Approximation by Stein s Method written by Louis H.Y. Chen and published by Springer Science & Business Media. This book was released on 2010-10-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Malliavin Calculus and Normal Approximations And Spatial Population Models written by David Nualart and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Malliavin Calculus written by David Nualart and published by Cambridge University Press. This book was released on 2018-09-27 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Download or read book Stochastic Analysis written by Hiroyuki Matsumoto and published by Cambridge University Press. This book was released on 2017 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.
Download or read book Selected Aspects of Fractional Brownian Motion written by Ivan Nourdin and published by Springer Science & Business Media. This book was released on 2013-01-17 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Stein s Method written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 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.
Download or read book Differentiable Measures and the Malliavin Calculus written by Vladimir Igorevich Bogachev and published by American Mathematical Soc.. This book was released on 2010-07-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book L vy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Download or read book Malliavin Calculus for L vy Processes and Infinite Dimensional Brownian Motion written by Horst Osswald and published by Cambridge University Press. This book was released on 2012-03 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Download or read book Normal Approximation and Asymptotic Expansions written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2010-11-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Fourier analysis, --
Download or read book Stochastic Calculus of Variations in Mathematical Finance written by Paul Malliavin and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly esteemed author Topics covered are relevant and timely
Download or read book Weak Approximations written by Arturo Kohatsu-Higa and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
