Diffusion Processes and Related Problems in Analysis, Volume I

I Infinite-dimensional Diffusion Processes.- Martin Boundaries on Wiener Space.- Hypoellipticity in Infinite Dimensions.- On Interacting Ornstein-Uhlenbeck Processes.- II Finite-dimensional Diffusion Processes.- Some Phenomena of the Characteristic Boundary Exit Problem.- Harmonic Measure for Random Genetic Drift.- Boundary Hitting Approximations for Markov Processes.- Brownian Motion in a Wedge with Variable Skew Reflection: II.- A Generalized Arc-sine Law and Nelson’s Stochastic Mechanics of One-dimensional Time-homogenous Diffusions.- III Diffusion Processes in Stochastic Analysis.- Some Regularity Results and Eigenfunction Estimates for the Schrödinger Operator.- On Estimating the Hypercontractive Constant of a Diffusion Process on a Compact Manifold.- Can the Schrödinger Equation be a Boltzmann Equation?.- A Stochastic Approach to Moving Boundary Problems.- Monotonicity Methods for White Noise Driven Quasilinear Stochastic Partial Differential Equations.- A Probabilistic Approach to the Heat Equation for the
$$\bar \partial \,$$
-Neumann Problem.- An Equivalence Theorem for Schrödinger Operators and its Applications.- IV Diffusion Processes in Geometry.- Stochastic Control Problems in Symmetric Cones and Spherical Functions.- Applications of Semigroup Domination.- A Degenerating Sequence of Riemannian Metrics on a Manifold and their Brownian Motions.- A Stochastic Criterion for Yang-Mills Connections.- V General Theory of Processes.- Dirichlet Forms and Markov Fields-A Report on Recent Developments.- Itô’s Formula for Stochastic Integration in Banach Spaces.- Regular, Stationary Gaussian Processes with the Markov Property of Infinite Order and Diffusive Filtrations.- Topics in the Theory of Noncausal Stochastic Integral Equations.- Orlicz and LuxemburgNorm Inequalities.- VI Large Deviations.- Large Deviations by the Asymptotic Value Method.- Cramér Functional Estimates for Gaussian Measures.- Asymptotic Behavior of the Laplace Transform of Weighted Occupation Times of Random Walks and Applications.