55 citations · 199 across the 14 of their papers we have counts for
9 papers · 1 filter
On a variance dependent Dvoretzky-Kiefer-Wolfowitz inequality
Daniel Bartl, Shahar Mendelson
Let be a real-valued random variable with distribution function . Set to be independent copies of and let be the corresponding empirical distribut…
The Wasserstein space of stochastic processes
Daniel Bartl, Mathias Beiglböck, Gudmund Pammer
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous a…
Limits of random walks with distributionally robust transition probabilities
Daniel Bartl, Stephan Eckstein, Michael Kupper
We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition…
Estimating processes in adapted Wasserstein distance
Julio Backhoff, Daniel Bartl, Mathias Beiglböck +1
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scienti…
Functional inequalities for forward and backward diffusions
Daniel Bartl, Ludovic Tangpi
In this article we derive Talagrand's inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic…
All Adapted Topologies are Equal
Julio Backhoff-Veraguas, Daniel Bartl, Mathias Beiglböck +1
A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology…