**Author**: Giuseppe Da Prato,Jerzy Zabczyk

**Publisher:**Cambridge University Press

**ISBN:**1139917153

**Category:**Mathematics

**Page:**N.A

**View:**3305

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# Search Results for: stochastic-equations-in-infinite-dimensions-encyclopedia-of-mathematics-and-its-applications

**Author**: Giuseppe Da Prato,Jerzy Zabczyk

**Publisher:** Cambridge University Press

**ISBN:** 1139917153

**Category:** Mathematics

**Page:** N.A

**View:** 3305

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.

**Author**: Guiseppe Da Prato,Jerzy Zabczyk

**Publisher:** Cambridge University Press

**ISBN:** 9780521059800

**Category:** Mathematics

**Page:** 454

**View:** 9818

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.
*with Applications to Stochastic Partial Differential Equations*

**Author**: Leszek Gawarecki,Vidyadhar Mandrekar

**Publisher:** Springer Science & Business Media

**ISBN:** 3642161944

**Category:** Mathematics

**Page:** 291

**View:** 8706

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**: Kai Liu

**Publisher:** CRC Press

**ISBN:** 9781420034820

**Category:** Mathematics

**Page:** 312

**View:** 4498

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.

**Author**: Giuseppe Da Prato,Luciano Tubaro

**Publisher:** CRC Press

**ISBN:** 9780203910177

**Category:** Mathematics

**Page:** 474

**View:** 4681

Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
*Dynamic Programming and HJB Equations*

**Author**: Giorgio Fabbri,Fausto Gozzi,Andrzej Święch

**Publisher:** Springer

**ISBN:** 3319530674

**Category:** Mathematics

**Page:** 916

**View:** 663

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

**Author**: Michael Grinfeld

**Publisher:** John Wiley & Sons

**ISBN:** 3527684271

**Category:** Science

**Page:** 632

**View:** 7747

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

**Author**: Sheung Tsun Tsou

**Publisher:** Academic Pr

**ISBN:** 9780125126601

**Category:** Science

**Page:** 3500

**View:** 6022

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Differential equations

**Page:** N.A

**View:** 7559

**Author**: Li Wang

**Publisher:** N.A

**ISBN:** N.A

**Category:** Hilbert space

**Page:** 146

**View:** 9648

*Mathematical, physical, and engineering sciences*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Engineering

**Page:** N.A

**View:** 3141

**Author**: Society for Industrial and Applied Mathematics

**Publisher:** N.A

**ISBN:** N.A

**Category:** Automatic control

**Page:** N.A

**View:** 6338

**Author**: René A. Carmona,Ivar Ekeland,Jean-Michel Lasry,Pierre-Louis Lions,Huyên Pham,Erik Taflin

**Publisher:** Springer

**ISBN:** N.A

**Category:** Mathematics

**Page:** 248

**View:** 6651

This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by René Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyên Pham.
*Differential inclusions, control and optimization*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Control theory

**Page:** N.A

**View:** 2743

*Series B.*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 6070

*Mathematics*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 6621

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Differential equations

**Page:** N.A

**View:** 6796

*An Evolution Equation Approach*

**Author**: S. Peszat,J. Zabczyk

**Publisher:** Cambridge University Press

**ISBN:** 0521879892

**Category:** Mathematics

**Page:** 419

**View:** 9056

Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

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