The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics
Download The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics
Author: Nicolai Victorovich Norin
language: en
Publisher: World Scientific
Release Date: 1996-08-30
This volume discusses the extended stochastic integral (ESI) (or Skorokhod-Hitsuda Integral) and its relation to the logarithmic derivative of differentiable measure along the vector or operator field. In addition, the theory of surface measures and the theory of heat potentials in infinite-dimensional spaces are discussed. These theories are closely related to ESI.It starts with an account of classic stochastic analysis in the Wiener spaces; and then discusses in detail the ESI for the Wiener measure including properties of this integral understood as a process. Moreover, the ESI with a nonrandom kernel is investigated.Some chapters are devoted to the definition and the investigation of properties of the ESI for Gaussian and differentiable measures.Surface measures in Banach spaces and heat potentials theory in Hilbert space are also discussed.
Differentiable Measures and the Malliavin Calculus
Author: Vladimir Igorevich Bogachev
language: en
Publisher: American Mathematical Soc.
Release Date: 2010-07-21
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.
The Non-uniform Riemann Approach To Stochastic Integration
Author: Varayu Boonpogkrong
language: en
Publisher: World Scientific
Release Date: 2024-09-17
This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.