Expectations and Martingales in Metric Spaces

Tom Christiansen, University of Bonn

Abstract. We develop a theory of martingales with values in metric spaces of nonpositive curvature. Our main results state existence of (continuous-time) martingales (X_{t})_{0≤t≤T} with given terminal data X_{T}. These processes will be constructed via time discretization. The notion of discrete-time martingale is based on the concept of iterated conditional barycenters. Moreover, in more specific spaces as Riemannian Simplicial complexes we develop a stochastic calculus and present martingale characterizations.