Introduction to Infinite Dimensional Stochastic Analysis

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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 088/5 ( reviews)

Introduction to Infinite Dimensional Stochastic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Infinite Dimensional Stochastic Analysis write by Zhi-yuan Huang. This book was released on 2012-12-06. Introduction to Infinite Dimensional Stochastic Analysis available in PDF, EPUB and Kindle. 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).

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

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Release : 2007-05-22
Genre : Mathematics
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Book Rating : 671/5 ( reviews)

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective write by René Carmona. This book was released on 2007-05-22. Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective available in PDF, EPUB and Kindle. This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM

Stochastic Equations in Infinite Dimensions

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Release : 2013-11-21
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Book Rating : 061/5 ( reviews)

Stochastic Equations in Infinite Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Equations in Infinite Dimensions write by Da Prato Guiseppe. This book was released on 2013-11-21. Stochastic Equations in Infinite Dimensions available in PDF, EPUB and Kindle. The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Ito and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations."

An Introduction to Infinite-Dimensional Analysis

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Release : 2006-08-25
Genre : Mathematics
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Book Rating : 214/5 ( reviews)

An Introduction to Infinite-Dimensional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Infinite-Dimensional Analysis write by Giuseppe Da Prato. This book was released on 2006-08-25. An Introduction to Infinite-Dimensional Analysis available in PDF, EPUB and Kindle. 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 starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.

Stochastic Differential Equations in Infinite Dimensions

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Release : 2010-11-29
Genre : Mathematics
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Book Rating : 944/5 ( reviews)

Stochastic Differential Equations in Infinite Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Differential Equations in Infinite Dimensions write by Leszek Gawarecki. This book was released on 2010-11-29. Stochastic Differential Equations in Infinite Dimensions available in PDF, EPUB and Kindle. The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.