Nine survey articles in this volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Key topics covered: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, martingale problem and Markov uniqueness of infinite- dimensional Nelson diffusions, analysis in geometric probability theory, measure-preserving shifts on the Wiener space, cohomology on loop spaces, and stochastic Volterra equations Contributors: H. Airault * L. Coutin * L. Decreusefond * C. Leonard * R. Leandre * P. Lescot * P. Malliavin * M. Oberguggenberger * R. Rebolledo * F. Russo * A.S. Ustunel * L. Wu The work, an outgrowth of a workshop on stochastic analysis held in Lisbon, serves as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, math physics, and physics. TOC:1. Complete positivity and open quantum systems (Rebolledo) * 2.Stochastic Volterra Equations w/ Singular Kernels(Coutin/Decreusefond) * 3. Properties of Measure-Preserving Shifts onthe Wiener Space (Ustunel) * 4. Singular Limiting Behavior inNonlinear Stochastic Wave Equations (Oberguggenberger/Russo) * 5.Mehler-type semigroups on Hilbert Spaces and their Generators (Lescot)* 6. Some Results on Entropic Projections (Leonard) * 7. Martingaleand Markov Uniqueness of Infinite DimensionalNelson's Diffusions (Wu)* 8. Functorial Analysis in Geometric Probability Theory(Airault/Malliavin) * 9. Stochastic Diffeology & Homotopy (Leandre)
