Geometry and Stochastic Calculus on Wasserstein spaces

Doctoral thesis (2010)

P ([0, 1])) with respect to the Skorohod topology. In the last chapter we restrict ourselves to the space of histograms on the unit interval. We calculate the Wasserstein distances numerically and obtain ... [more ▼]

P ([0, 1])) with respect to the Skorohod topology. In the last chapter we restrict ourselves to the space of histograms on the unit interval. We calculate the Wasserstein distances numerically and obtain a Riemannian metric on the simplex. We investigate explosion behaviour of the respective diffusion processes in dimension 1 and 2. [less ▲]