Diffusion Processes and Related Problems in Analysis, Volume I: Diffusions in Analysis and Geometry

ISBN-13: 9781468405668 / Angielski / Miękka / 2012 / 521 str.

Pinsky

Opis

During the week of October 23-27,1989, Northwestern University hosted an international conference on the theme "Diffusion Processes and Related Problems in Analysis." This was attended by 105 partici- pants representing 14 different countries. The conference, which is part of the "Emphasis Year" program traditionally supported by the Mathematics Department, was additionally supported by grants from the National Science Foundation, the National Security Agency, the Institute for Mathematics and Applications, as well as by supplemen- tary sources from Northwestern University. The purpose of this meeting was to bring together workers in vari- ous parts of probability theory, mathematical physics, and partial dif- ferential equations. Previous efforts in this direction were represented by the 1987 AMS Summer Research Conference "Geometry of Random Motion" co-sponsored with Rick Durrett, the proceedings of which ap- peared as volume 73 in the AMS series "Contemporary Mathematics." The present effort is intended to extend beyond the strictly geometric theme and to include problems of large deviations, stochastic flows, and other areas of stochastic analysis in which diffusion processes play a leading role.

Spis treści

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 Luxemburg Norm 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.