Estimating processes in adapted Wasserstein distance

A number of researchers have independently introduced topologies on the set laws stochastic processes that extend usual weak topology. Depending respective scientific background this was motivated by applications and connections to various areas (e.g., Plug–Pichler—stochastic programming, Hellwig—game theory, Aldous—stability optimal stopping, Hoover–Keisler—model theory). Remarkably, all these seemingly independent approaches define same adapted topology in finite discrete time. Our first main result is construct an variant empirical measure consistently estimates full generality. natural compatible metric for given refinement Wasserstein distance, as established seminal works Pflug–Pichler. Specifically, distance allows control error optimization problems, pricing hedging stopping etcetera a Lipschitz fashion. The second article yields quantitative bounds convergence with respect distance. Surprisingly, we obtain virtually rates concentration results are known classical wrt.