Introduction to Infinite Dimensional Stochastic Analysis

Introduction to Infinite Dimensional Stochastic Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 308
Release :
ISBN-10 : 9789401141086
ISBN-13 : 9401141088
Rating : 4/5 (088 Downloads)

Book Synopsis Introduction to Infinite Dimensional Stochastic Analysis by : Zhi-yuan Huang

Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).


Introduction to Infinite Dimensional Stochastic Analysis Related Books

Introduction to Infinite Dimensional Stochastic Analysis
Language: en
Pages: 308
Authors: Zhi-yuan Huang
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematic
Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective
Language: en
Pages: 236
Authors: René Carmona
Categories: Mathematics
Type: BOOK - Published: 2007-05-22 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution e
Stochastic Equations in Infinite Dimensions
Language: en
Pages:
Authors: Da Prato Guiseppe
Categories:
Type: BOOK - Published: 2013-11-21 - Publisher:

DOWNLOAD EBOOK

The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typical
An Introduction to Infinite-Dimensional Analysis
Language: en
Pages: 217
Authors: Giuseppe Da Prato
Categories: Mathematics
Type: BOOK - Published: 2006-08-25 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It sta
Stochastic Differential Equations in Infinite Dimensions
Language: en
Pages: 300
Authors: Leszek Gawarecki
Categories: Mathematics
Type: BOOK - Published: 2010-11-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical pr