Stochastic Partial Differential Equations and Applications

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