Author: Kiyosi Ito
Publisher: SIAM
ISBN: 9781611970234
Category : Mathematics
Languages : en
Pages : 79
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Book Description
A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
Author: Kiyosi Itô
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: G. Kallianpur
Publisher: IMS
ISBN: 9780940600386
Category : Mathematics
Languages : en
Pages : 356
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Book Description
Author: Kai Liu
Publisher: CRC Press
ISBN: 1420034820
Category : Mathematics
Languages : en
Pages : 311
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Book Description
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
Author: Giuseppe Da Prato
Publisher: Cambridge University Press
ISBN: 1107055849
Category : Mathematics
Languages : en
Pages : 513
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Book Description
Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
Author: H Kunita
Publisher: CRC Press
ISBN: 9780582244900
Category : Mathematics
Languages : en
Pages : 340
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Book Description
The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)
Author: Leszek Gawarecki
Publisher: Springer
ISBN: 9783642266348
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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.
Author: G. Kallianpur
Publisher:
ISBN:
Category : Stochastic differential equations
Languages : en
Pages : 345
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Book Description
This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.
Author: Wilfried Grecksch
Publisher: World Scientific
ISBN: 9811209804
Category : Science
Languages : en
Pages : 261
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Book Description
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Author: Da Prato Guiseppe
Publisher:
ISBN: 9781306148061
Category :
Languages : en
Pages :
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Book Description
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."
