Presents an overview of stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. This book includes such topics as Navier-Stokes equations, Ornstein-Uhlenbeck semigroups, and quantum stochastic differential equations. It offers information for PhD students in probability.

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. Levy 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 Levy Noise. Qualitative Properties of Solutions to Stochastic Burgers' System of Euqations. On the Stochastic Fubini Theorem in Infinite Dimensions. Ito-Tanaka's Formula for SPDEs Driven by Additive Space-Time White Noise.