Stochastic Processes - Mathematics and Physics: Proceedings of the 1st BiBoS-Symposium held in Bielefeld, West Germany, September 10-15, 1984

ISBN-13: 9783540159988 / Angielski / Miękka / 1986 / 260 str.

Sergio Albeverio;Phillippe Blanchard;Ludwig Streit

Opis

This second BiBoS volume surveys recent developments in the theory of stochastic processes. Particular attention is given to the interaction between mathematics and physics.
Main topics include: statistical mechanics, stochastic mechanics, differential geometry, stochastic proesses, quantummechanics, quantum field theory, probability measures, central limit theorems, stochastic differential equations, Dirichlet forms.

Spis treści

Stochastic lie group-valued measures and their relations to stochastic curve integrals, gauge fields and markov cosurfaces.- Existence and sample path properties of the diffusions in Nelson's stochastic mechanics.- Characteristic exponents for stochastic flows.- Electric field and effective dielectric constant in random media with non-linear response.- Remarks on the central limit theorem for weakly dependent random variables.- Time reversal on Wiener space.- Lattice gauge theory; Heuristics and convergence.- The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation.- An elementary approach to Brownian motion on manifolds.- The stochastic mechanics of the ground-state of the hydrogen atom.- Nonstandard analysis and perturbations of the laplacian along Brownian paths.- Haussdorf dimension for the statistical equilibrium of stochastics flows.- Stopping problems of symmetric Markov processes and non-linear variational inequalites.- Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods.- Rigorous scaling laws for Dyson measures.- Asymptotic freedom: A rigorous approach.- The fermion stochastic calculus I.