Wiener processes on manifolds of maps

Abstract

Synopsis The solutions of stochastic differential equations are used to construct Markov processes on the Banach manifold C ( S, M ) of continuous maps from a compact metric space S into a smooth complete finite dimensional Riemannian manifold M . In the special case where S is a single point the construction gives a large class of diffusion processes on the manifold M , including (under certain curvature conditions) the Brownian motion process.