Advances in Analysis, Probability and Mathematical Physics

Table of Content.- I: Analysis.- Singular traces and nonstandard analysis.- Navier-Stokes equations.- Hyperfinite approximations of commutative topological groups.- A note on the myope topology.- Nonlinear theories of generalized functions.- A nonstandard approach to the Pettis integral.- A counterexample to the spectral mapping theorem revisited from a nonstandard point of view.- Nonstandard polynominals in several variables.- An existence result for a class of partial differential equations with smooth coefficients.- On the generation of topology by external equivalence relations.- Nonstandard hulls of Lebesgue-Bochner spaces.- II: Probability Theory.- A nonstandard approach to diffusions on manifolds and nonstandard heat kernels.- A nonstandard approach to the Malliavin Calculus.- Ergodic transformations in AST.- Nonstandard characterization for a general invariance principle.- Andersons’s Brownian motion and the infinite dimensional Ornstein-Uhlenbeck process.- Two applications of NSA in the theory of stochastic dynamical systems.- Nonstandard methods and the space of experiments.- III: Mathematical Physics.- Infinite range forces and strong L1-asymptotics for the space-homogeneous Boltzmann equation.- A nonstandard analysis approach to the theory of quantum meanfield systems.