Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this book presents valuable information for PhD students in probability and PDEs as well as for researchers in pure and applied mathematics. Coverage includes Navier-Stokes equations, Ornstein-Uhlenbeck semigroups, quantum stochastic differential equations, applications of SPDE, 3D stochastic Navier-Stokes equations, and nonlinear filtering.
Table of Contents
Weak, Strong, and 4 Semigroup Solutions of Classical SDE: An Example. Feynman Path Integrals for Time-Dependent Potentials. The Irreducibility of Transition Semigroups and Approximate Controllability. Gradient Bounds for Solutions of Elliptic and Parabolic Equations. Asymptotic Compactness and Absorbing Sets for Stochastic Burgers Equations Driven by Space Time White Noise and for Some 2D Stochastic Navier-Stokes Equations on Certain Unbounded Domains. A Characterization of Approximately-Controllable Linear Stochastic Differential Equations. Asymptotic Behavior of Systems of DPDEs with Multiplicative Noise. On L1(H,m)-Properties of Ornstein-Uhlenbeck Semigroups. Intertwining and the Markov Uniqueness Problem on Path Spaces. On Some Problems of Regularity in Two-Dimensional Stochastic Hydrodynamics. Two Models of K41. Exponential Ergodicity for Stochastic Reaction-Diffusion Equations. Stochastic Optimal Control of Delay Equations Arising in Advertising Models. On Acceleration of Approximation Methods. Stochastic Variational Equations in White Noise Analysis. On the Foundation of the Lp-Theory of SPDEs. Lévy Noises and Stochastic Integrals on Banach Spaces. A Stabilization Phenomenon for a Class of Stochastic Partial Differential Equations. Stochastic Heat and Wave Equations Driven by an Impulsive Noise. Harmonic Functions for Generalized Mehler Semigroups. The Dynamics of the 3D Navier-Stokes Equations. Stochastic Navier-Stokes Equations: Solvability, Control, and Filtering. Stability of the Optimal Filter Via Pointwise Gradient Estimates. Fractal Burgers Equation Driven by Lévy Noise. Qualitative Properties of Solutions to Stochastic Burgers' System of Euqations. On the Stochastic Fubini Theorem in Infinite Dimensions. Itô-Tanaka's Formula for SPDEs Driven by Additive Space-Time White Noise.