Stochastic Partial Differential Equations and Applications: 1st Edition (Paperback) book cover

Stochastic Partial Differential Equations and Applications

1st Edition

Edited by Giuseppe Da Prato, Luciano Tubaro

CRC Press

474 pages

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Paperback: 9780824707927
pub: 2002-04-05
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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.

Reviews

"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

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

About the Series

Lecture Notes in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations