Stochastic Pdes And Kolmogorov Equations In Infinite Dimensions

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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Author : N.V. Krylov
Publisher : Springer
ISBN 13 : 3540481613
Total Pages : 248 pages
Book Rating : 4.5/5 (44 download)

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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.

Stochastic Equations in Infinite Dimensions

Author : Giuseppe Da Prato
Publisher : Cambridge University Press
ISBN 13 : 1139917153
Total Pages : 513 pages
Book Rating : 4.1/5 (399 download)

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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 Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part 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. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.

Stochastic Equations in Infinite Dimensions

Author : Giuseppe Da Prato
Publisher : Cambridge University Press
ISBN 13 : 1107055849
Total Pages : 513 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Stochastic Equations in Infinite Dimensions by : Giuseppe Da Prato

Second Order PDE's in Finite and Infinite Dimension

Author : Sandra Cerrai
Publisher : Springer
ISBN 13 : 3540451471
Total Pages : 332 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Second Order PDE's in Finite and Infinite Dimension by : Sandra Cerrai

Download or read book Second Order PDE's in Finite and Infinite Dimension written by Sandra Cerrai and published by Springer. This book was released on 2003-07-01 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap.

Stochastic Differential Equations in Infinite Dimensions

Author : Leszek Gawarecki
Publisher : Springer
ISBN 13 : 9783642266348
Total Pages : 291 pages
Book Rating : 4.2/5 (663 download)

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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.

Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Author :
Publisher :
ISBN 13 :
Total Pages : 239 pages
Book Rating : 4.:/5 (86 download)

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Book Synopsis Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by :

Download or read book Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions written by and published by . This book was released on 1999 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics

Author : Wilfried Grecksch
Publisher : World Scientific
ISBN 13 : 9811209804
Total Pages : 261 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics by : Wilfried Grecksch

Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces

Author : Kiyosi Ito
Publisher : SIAM
ISBN 13 : 9781611970234
Total Pages : 79 pages
Book Rating : 4.9/5 (72 download)

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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.

Stochastic Equations in Infinite Dimensions

Author : Da Prato Guiseppe
Publisher :
ISBN 13 : 9781306148061
Total Pages : pages
Book Rating : 4.1/5 (48 download)

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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."

Stochastic Equations in Infinite Dimensions

Author : Guiseppe Da Prato
Publisher : Cambridge University Press
ISBN 13 : 9780521059800
Total Pages : 476 pages
Book Rating : 4.0/5 (598 download)

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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.

Stochastic Equations in Infinite Dimensions, Second Edition

Author : Giuseppe Da Prato
Publisher :
ISBN 13 : 9781139905466
Total Pages : pages
Book Rating : 4.9/5 (54 download)

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Book Synopsis Stochastic Equations in Infinite Dimensions, Second Edition by : Giuseppe Da Prato

Download or read book Stochastic Equations in Infinite Dimensions, Second Edition written by Giuseppe Da Prato and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Infinite Dimensional Stochastic Analysis

Author : Zhi-yuan Huang
Publisher : Springer Science & Business Media
ISBN 13 : 9401141088
Total Pages : 308 pages
Book Rating : 4.4/5 (11 download)

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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).

An Introduction to Infinite-Dimensional Analysis

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
ISBN 13 : 3540290214
Total Pages : 208 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis An Introduction to Infinite-Dimensional Analysis by : Giuseppe Da Prato

Download or read book An Introduction to Infinite-Dimensional Analysis written by Giuseppe Da Prato and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastics in Finite and Infinite Dimensions

Author : Takeyuki Hida
Publisher : Springer Science & Business Media
ISBN 13 : 1461201675
Total Pages : 436 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastics in Finite and Infinite Dimensions by : Takeyuki Hida

Download or read book Stochastics in Finite and Infinite Dimensions written by Takeyuki Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.

Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Author : Nikolaĭ Vladimirovich Krylov
Publisher :
ISBN 13 :
Total Pages : 239 pages
Book Rating : 4.:/5 (99 download)

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Book Synopsis Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by : Nikolaĭ Vladimirovich Krylov

Download or read book Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions written by Nikolaĭ Vladimirovich Krylov and published by . This book was released on 1999 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Differential Equations in Infinite Dimensional Spaces

Author : G. Kallianpur
Publisher : IMS
ISBN 13 : 9780940600386
Total Pages : 356 pages
Book Rating : 4.6/5 (3 download)

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Book Synopsis Stochastic Differential Equations in Infinite Dimensional Spaces by : G. Kallianpur

Download or read book Stochastic Differential Equations in Infinite Dimensional Spaces written by G. Kallianpur and published by IMS. This book was released on 1995 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Partial Differential Equations

Author : Sergey V. Lototsky
Publisher : Springer
ISBN 13 : 3319586475
Total Pages : 508 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Stochastic Partial Differential Equations by : Sergey V. Lototsky

Download or read book Stochastic Partial Differential Equations written by Sergey V. Lototsky and published by Springer. This book was released on 2017-07-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.