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Author: Kai Liu
Publisher: Cambridge University Press
Published: 2019-05-02
Total Pages: 277
ISBN-13: 1108705170
DOWNLOAD EBOOKPresents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.
Author: Rafail Khasminskii
Publisher: Springer Science & Business Media
Published: 2011-09-20
Total Pages: 353
ISBN-13: 3642232809
DOWNLOAD EBOOKSince the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
Author: Kai Liu
Publisher: Cambridge University Press
Published: 2019-05-02
Total Pages: 277
ISBN-13: 1108626491
DOWNLOAD EBOOKThe stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.
Author: Rafail Khasminskii
Publisher: Springer
Published: 2011-09-25
Total Pages: 342
ISBN-13: 9783642232817
DOWNLOAD EBOOKSince the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
Author: Kai Liu
Publisher: CRC Press
Published: 2005-08-23
Total Pages: 311
ISBN-13: 1420034820
DOWNLOAD EBOOKStochastic 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: G. Kallianpur
Publisher: IMS
Published: 1995
Total Pages: 356
ISBN-13: 9780940600386
DOWNLOAD EBOOKAuthor: Simo Särkkä
Publisher: Cambridge University Press
Published: 2019-05-02
Total Pages: 327
ISBN-13: 1316510085
DOWNLOAD EBOOKWith this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author: T. E. Govindan
Publisher: Springer Nature
Published:
Total Pages: 321
ISBN-13: 3031427912
DOWNLOAD EBOOKAuthor: Kiyosi Ito
Publisher: SIAM
Published: 1984-01-01
Total Pages: 79
ISBN-13: 9781611970234
DOWNLOAD EBOOKA 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: Leszek Gawarecki
Publisher: Springer Science & Business Media
Published: 2010-11-29
Total Pages: 300
ISBN-13: 3642161944
DOWNLOAD EBOOKThe 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.
