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Trotter Kato Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications
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Book Synopsis Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications by : T. E. Govindan
Download or read book Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer Nature. This book was released on with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications by : T. E. Govindan
Download or read book Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer. This book was released on 2016-11-11 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.
Book Synopsis Stochastic Differential Equations in Infinite Dimensions by : Leszek Gawarecki
Download or read book Stochastic Differential Equations in Infinite Dimensions written by Leszek Gawarecki and published by Springer. This book was released on 2013-01-27 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Probability and Stochastic Processes by : V. C. Joshua
Download or read book Applied Probability and Stochastic Processes written by V. C. Joshua and published by Springer Nature. This book was released on 2020-08-29 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected papers presented at the International Conference on Advances in Applied Probability and Stochastic Processes, held at CMS College, Kerala, India, on 7–10 January 2019. It showcases high-quality research conducted in the field of applied probability and stochastic processes by focusing on techniques for the modelling and analysis of systems evolving with time. Further, it discusses the applications of stochastic modelling in queuing theory, reliability, inventory, financial mathematics, operations research, and more. This book is intended for a broad audience, ranging from researchers interested in applied probability, stochastic modelling with reference to queuing theory, inventory, and reliability, to those working in industries such as communication and computer networks, distributed information systems, next-generation communication systems, intelligent transportation networks, and financial markets.
Book Synopsis Yosida Approximations for Multivalued Stochastic Differential Equations in Finite and Infinite Dimensions with Applications by : Matthias Stephan
Download or read book Yosida Approximations for Multivalued Stochastic Differential Equations in Finite and Infinite Dimensions with Applications written by Matthias Stephan and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Infinite Dimensional Stochastic Differential Equations with Applications by : Kai Liu
Download or read book Stability of Infinite Dimensional Stochastic Differential Equations with Applications written by Kai Liu and published by CRC Press. This book was released on 2019-09-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings. This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. In recent years, this area of study has become the focus of increasing attention, and the relevant literature has expanded greatly. Stability of Infinite Dimensional Stochastic Differential Equations with Applications makes up-to-date material in this important field accessible even to newcomers and lays the foundation for future advances.
Book Synopsis Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces by : Kiyosi Ito
Download or read book Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces written by Kiyosi Ito and published by SIAM. This book was released on 1984-01-01 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Approximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions by : Krystyna Twardowska
Download or read book Approximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions written by Krystyna Twardowska and published by . This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite Dimensional Stochastic Differential Equations with Applications by : G. Kallianpur
Download or read book Infinite Dimensional Stochastic Differential Equations with Applications written by G. Kallianpur and published by . This book was released on 1989 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Second Order Partial Differential Equations in Hilbert Spaces by : Giuseppe Da Prato
Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2002-07-25 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Guiseppe Da Prato
Download or read book Stochastic Equations in Infinite Dimensions written by Guiseppe Da Prato and published by Cambridge University Press. This book was released on 2008-02-04 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of the 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 Itô and Gikhman 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 measures 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.
Book Synopsis Stochastic Differential Equations in Infinite Dimensional Spaces and Their Applications by : J. R. Dorrah
Download or read book Stochastic Differential Equations in Infinite Dimensional Spaces and Their Applications written by J. R. Dorrah and published by . This book was released on 1984 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Equations in Infinite Dimensions by : Da Prato Guiseppe
Download or read book Stochastic Equations in Infinite Dimensions written by Da Prato Guiseppe and published by . This book was released on 2013-11-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Stability of Stochastic Differential Equations in Infinite Dimensions by : Kai Liu
Download or read book Stability of Stochastic Differential Equations in Infinite Dimensions written by Kai Liu and published by . This book was released on 2004* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by : N.V. Krylov
Download or read book Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions written by N.V. Krylov and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Giuseppe Da Prato
Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by . This book was released on 2014-05-22 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of the 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 Gikhman 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 measures 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.
Book Synopsis Stochastic Differential Equations and Applications by : X Mao
Download or read book Stochastic Differential Equations and Applications written by X Mao and published by Elsevier. This book was released on 2007-12-30 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. - Has been revised and updated to cover the basic principles and applications of various types of stochastic systems - Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists
