40 citations · 295 across the 45 of their papers we have counts for
4 papers · 1 filter
The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations
Zdzisław Brzeźniak, Mario Maurelli, Alexander Schmeding
The Ebin-Marsden theory is a powerful geometric framework for many PDEs from fluid dynamics. In this paper we provide a toolbox to apply the Ebin-Marsden approach to stochastic PDE…
The geometry of controlled rough paths
Mazyar Ghani Varzaneh, Sebastian Riedel, Alexander Schmeding +1
We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dime…
Geometric rough paths on infinite dimensional spaces
Erlend Grong, Torstein Nilssen, Alexander Schmeding
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For , we give criteria for whe…
Incompressible Euler equations with stochastic forcing: a geometric approach
Mario Maurelli, Klas Modin, Alexander Schmeding
We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact m…