Stochastic Cauchy Problems In Infinite Dimensions PDF Download
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Author | : Irina V. Melnikova |
Publisher | : CRC Press |
Total Pages | : 232 |
Release | : 2018-09-03 |
Genre | : Mathematics |
ISBN | : 1315360268 |
Download Stochastic Cauchy Problems in Infinite Dimensions Book in PDF, ePub and Kindle
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Author | : Leszek Gawarecki |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2010-11-29 |
Genre | : Mathematics |
ISBN | : 3642161944 |
Download Stochastic Differential Equations in Infinite Dimensions Book in PDF, ePub and Kindle
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 | : Giuseppe Da Prato |
Publisher | : Cambridge University Press |
Total Pages | : 513 |
Release | : 2014-04-17 |
Genre | : Mathematics |
ISBN | : 1139917153 |
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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 | : Giuseppe Da Prato |
Publisher | : Cambridge University Press |
Total Pages | : 513 |
Release | : 2014-04-17 |
Genre | : Mathematics |
ISBN | : 1107055849 |
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Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
Author | : G. Kallianpur |
Publisher | : IMS |
Total Pages | : 356 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9780940600386 |
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Author | : Hui-Hsiung Kuo |
Publisher | : World Scientific |
Total Pages | : 257 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9812779558 |
Download Infinite Dimensional Stochastic Analysis Book in PDF, ePub and Kindle
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians. Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (425 KB). Contents: Complex White Noise and the Infinite Dimensional Unitary Group (T Hida); Complex It Formulas (M Redfern); White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta); Probability Measures with Sub-Additive Principal SzegAOCoJacobi Parameters (A Stan); Donsker''s Functional Calculus and Related Questions (P-L Chow & J Potthoff); Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.); Adapted Solutions to the Backward Stochastic NavierOCoStokes Equations in 3D (P Sundar & H Yin); Spaces of Test and Generalized Functions of Arcsine White Noise Formulas (A Barhoumi et al.); An Infinite Dimensional Fourier-Mehler Transform and the L(r)vy Laplacian (K Saito & K Sakabe); The Heat Operator in Infinite Dimensions (B C Hall); Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha); White Noise Analysis in the Theory of Three-Manifold Quantum Invariants (A Hahn); A New Explicit Formula for the Solution of the BlackOCoMertonOCoScholes Equation (J A Goldstein et al.); Volatility Models of the Yield Curve (V Goodman). Readership: Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematic
Author | : H Kunita |
Publisher | : CRC Press |
Total Pages | : 340 |
Release | : 1994-08-22 |
Genre | : Mathematics |
ISBN | : 9780582244900 |
Download Stochastic Analysis on Infinite Dimensional Spaces Book in PDF, ePub and Kindle
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 | : Giuseppe Da Prato |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : |
ISBN | : 9781139905466 |
Download Stochastic Equations in Infinite Dimensions, Second Edition Book in PDF, ePub and Kindle
Author | : N. M. Chuong |
Publisher | : World Scientific |
Total Pages | : 372 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9812770496 |
Download Advances in Deterministic and Stochastic Analysis Book in PDF, ePub and Kindle
This volume collects articles in pure and applied analysis, partial differential equations, geometric analysis and stochastic and infinite-dimensional analysis. In particular, the contributors discuss integral and pseudo-differential operators, which play an important role in partial differential equations. Other methods of solving the partial differential equations are considered, such as the min-max approach to variational problems and boundary value problems. The foundations of quantum mechanics from the viewpoints of infinite-dimensional spaces and Bell''s inequality and contraction are also mentioned.
Author | : |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : 9814472239 |
Download Infinite Dimensional Stochastic Analysis Book in PDF, ePub and Kindle