Stochastic Partial Differential Equations and Applications  book cover
1st Edition

Stochastic Partial Differential Equations and Applications

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ISBN 9780824707927
Published April 5, 2002 by CRC Press
476 Pages

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Book Description

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.

Table of Contents

The Semi-Martingale Property of the Square of White Noise Integrators
Luigi Accardi and Andreas Boukas
SPDEs Leading to Local, Relativistic Quantum Vector Fields with Indefinite Metric and Nontrivial S-Matrix
Sergio Albeverio, Hanno Gottschalk, and Jiang-Lun Wu
Considerations on the Controllability of Stochastic Linear Heat Equations
Viorel Barbu and Gianmario Tessitore
Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements
Alberto Barchielli and Anna Maria Paganoni
Invariant Measures of Diffusion Processes: Regularity, Existence, and Uniqueness Problems
Vladimir I. Bogachev and Michael Röckner

On the Theory of Random Attractors and Some Open Problems
Tomas Caraballo and José Antonio Langa
Invariant Densities for Stochastic Semilinear Evolution Equations and Related Properties of Transition Semigroups
Anna Chojnowska-Michalik
On Some Generalized Solutions of Stochastic PDEs
Pao-Liu Chow
Riemannian Geometry on the Path Space
B. Cruzeiro and P. Malliavin
A Note on Regularizing Properties of Ornstein-Uhlenbeck Semigroups in Infinite Dimensions
Giuseppe Da Prato, Marco Fuhrman, and Jerzy Zabczyk
White Noise Approach to Stochastic Partial Differential Equations
T. Deck, S. Kruse, J. Potthoff, and H. Watanabe
Some Results on Invariant States for Quantum Markov Semigroups
Franco Fagnola and Rolando Rebolledo
Stochastic Problems in Fluid Dynamics
Franco Flandoli
Limit Theorems for Random Interface Models of Ginzburg-Landau "j Type
Giambattista Giacomin
Second Order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Optimal Control
Fausto Gozzi
Approximations of Stochastic Partial Differential Equations
István Gyöngy
Regularity and Continuity of Solutions to Stochastic Evolution Equations
Anna Karczewska
Some New Results in the Theory of SPDEs in Sobolev Spaces
N. V. Krylov
Lyapunov Function Approaches and Asymptotic Stability of Stochastic Evolution Equations in Hilbert Spaces-A Survey of Recent Developments
Kai Liu and Aubrey Truman
Strong Feller Infinite-Dimensional Diffusions
Bohdan Maslowski and Jan Seidler
Optimal Stopping Time and Impulse Control Problems for the Stochastic Navier-Stokes Equations
J. L. Menaldi and S. S. Sritharan
On Martingale Problem Solutions for Stochastic Navier-Stokes Equation
R. Mikulevicius and B. Rozovskii
SPDEs Driven by a Homogeneous Wiener Process
Szymon Peszat
Applications of Malliavin Calculus to SPDEs
Marta Sanz-Solé
Stochastic Curvature Driven Flows
Nung Kwan Yip

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"The book contains 25 contributions (of about twenty pages each) including new results as well as surveys and reviews of problems in questions so that the reader can get a feeling of what is the up-to-date state of knowledge in the respective areas. This is why the book can serve as a source for new ways of research as well as a digest for professionals working in SPDE's."
- Mathematica Bohemia