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.

chapter |20 pages

The Semi-Martingale Property of the Square of White Noise Integrators

ByLuigi Accardi, Andreas Boukas

chapter |18 pages

SPDEs Leading to Local, Relativistic Quantum Vector Fields with Indefinite Metric and Nontrivial S-Matrix

BySergio Albeverio, Hanno Gottschalk, Jiang-Lun Wu

chapter |14 pages

Considerations on the Controllability of Stochastic Linear Heat Equations

ByViorel Barbu, Gianmario Tessitore

chapter |16 pages

Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements

ByAlberto Barchielli, Anna Maria Paganoni

chapter |20 pages

Invariant Measures of Diffusion Processes: Regularity, Existence, and Uniqueness Problems

ByVladimir I. Bogachev, Michael Röckner

chapter |16 pages

On the Theory of Random Attractors and Some Open Problems

ByTomas Caraballo, José Antonio Langa

chapter |12 pages

On Some Generalized Solutions of Stochastic PDEs

ByPao-Liu Chow

chapter |34 pages

Riemannian Geometry on the Path Space

ByA. B. Cruzeiro, P. Malliavin

chapter |16 pages

A Note on Regularizing Properties of Ornstein — Uhlenbeck Semigroups in Infinite Dimensions

ByGiuseppe Da Prato, Marco Fuhrman, Jerzy Zabczyk

chapter |14 pages

White Noise Approach to Stochastic Partial Differential Equations

ByT. Deck, S. Kruse, J. Potthoff, H. Watanabe

chapter |12 pages

Some Results on Invariant States for Quantum Markov Semigroups

ByFranco Fagnola, Rolando Rebolledo

chapter |26 pages

Stochastic Problems in Fluid Dynamics

ByFranco Flandoli

chapter |20 pages

Limit Theorems for Random Interface Models of Ginzburg-Landau ∇ φ type

ByGiambattista Giacomin

chapter |22 pages

Approximations of Stochastic Partial Differential Equations

ByIstván Gyöngy

chapter |12 pages

Some New Results in the Theory of SPDEs in Sobolev Spaces

ByN.V. Krylov

chapter |16 pages

Strong Feller Infinite-Dimensional Diffusions 1

ByBohdan Maslowski, Jan Seidler

chapter |12 pages

On Martingale Problem Solutions for Stochastic Navier-Stokes Equation

ByR. Mikulevicius, B. Rozovskii

chapter |11 pages

SPDEs Driven by a Homogeneous Wiener Process

BySzymon Peszat

chapter |14 pages

Applications of Malliavin Calculus to SPDE’S

ByMarta Sanz-Solé

chapter |18 pages

Stochastic Curvature Driven Flows

ByNung Kwan Yip