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E-raamat: Stochastic Partial Differential Equations and Applications

Edited by (Scuola Normale Superiore, Pisa, Italy)
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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.

Arvustused

"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

Preface iii
Contributors vii
1 The Semi-Martingale Property of the Square of White Noise Integrators
1(20)
Luigi Accardi
Andreas Boukas
2 SPDEs Leading to Local, Relativistic Quantum Vector Fields with Indefinite Metric and Nontrivial S-Matrix
21(18)
Sergio Albeverio
Hanno Gottschalk
Jiang-Lun Wu
3 Considerations on the Controllability of Stochastic Linear Heat Equations
39(14)
Viorel Barbu
Gianmario Tessitore
4 Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements
53(16)
Alberto Barchielli
Anna Maria Paganoni
5 Invariant Measures of Diffusion Processes: Regularity, Existence, and Uniqueness Problems
69(20)
Vladimir I. Bogachev
Michael Rockner
6 On the Theory of Random Attractors and Some Open Problems
89(16)
Tomas Caraballo
Jose Antonio Langa
7 Invariant Densities for Stochastic Semilinear Evolution Equations and Related Properties of Transition Semigroups
105(16)
Anna Chojnowska-Michalik
8 On Some Generalized Solutions of Stochastic PDEs
121(12)
Pao-Liu Chow
9 Riemannian Geometry on the Path Space
133(34)
A. B. Cruzeiro
P. Malliavin
10 A Note on Regularizing Properties of Ornstein-Uhlenbeck Semigroups in Infinite Dimensions
167(16)
Giuseppe Da Prato
Marco Fuhrman
Jerzy Zabczyk
11 White Noise Approach to Stochastic Partial Differential Equations
183(14)
T. Deck
S. Kruse
J. Potthoff
H. Watanabe
12 Some Results on Invariant States for Quantum Markov Semigroups
197(12)
Franco Fagnola
Rolando Rebolledo
13 Stochastic Problems in Fluid Dynamics
209(26)
Franco Flandoli
14 Limit Theorems for Random Interface Models of Ginzburg-Landau Vφ Type
235(20)
Giambattista Giacomin
15 Second Order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Optimal Control
255(32)
Fausto Gozzi
16 Approximations of Stochastic Partial Differential Equations
287(22)
Istvan Gyongy
17 Regularity and Continuity of Solutions to Stochastic Evolution Equations
309(16)
Anna Karczewska
18 Some New Results in the Theory of SPDEs in Sobolev Spaces
325(12)
N. V. Krylov
19 Lyapunov Function Approaches and Asymptotic Stability of Stochastic Evolution Equations in Hilbert Spaces---A Survey of Recent Developments
337(36)
Kai Liu
Aubrey Truman
20 Strong Feller Infinite-Dimensional Diffusions
373(16)
Bohdan Maslowski
Jan Seidler
21 Optimal Stopping Time and Impulse Control Problems for the Stochastic Navier-Stokes Equations
389(16)
J. L. Menaldi
S. S. Sritharan
22 On Martingale Problem Solutions for Stochastic Navier-Stokes Equation
405(12)
R. Mikulevicius
B. Rozovskii
23 SPDEs Driven by a Homogeneous Wiener Process
417(12)
Szymon Peszat
24 Applications of Malliavin Calculus to SPDEs
429(14)
Marta Sanz-Sole
25 Stochastic Curvature Driven Flows
443
Nung Kwan Yip
Giuseppe Da Prato