7 papers · 1 filter
The Fundamental Theorem of Weak Optimal Transport
Mathias Beiglböck, Gudmund Pammer, Lorenz Riess +1
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Breni…
The Wasserstein Space of Stochastic Processes in Continuous Time
Daniel Bartl, Mathias Beiglböck, Gudmund Pammer +2
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the…
A note on the adapted weak topology in discrete time
Gudmund Pammer
The adapted weak topology is an extension of the weak topology for stochastic processes designed to adequately capture properties of underlying filtrations. With the recent work of…
Faking Brownian motion with continuous Markov martingales
Mathias Beiglböck, George Lowther, Gudmund Pammer +1
Hamza-Klebaner posed the problem of constructing martingales with Brownian marginals that differ from Brownian motion, so called fake Brownian motions. Besides its theoretical appe…
Applications of weak transport theory
Julio Daniel Backhoff-Veraguas, Gudmund Pammer
Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali introduced a transport problem for `weak' cost functionals. Basic results of optimal transp…
Stability of martingale optimal transport and weak optimal transport
Julio Backhoff-Veraguas, Gudmund Pammer
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans converges weakly to a transpo…