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.
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.
Reviews for Stochastic Partial Differential Equations and Applications
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
