… is an arbitrary subspace, denote by Wo the subspace of all elements u e W such that is a
compact subset contained in U, and by Wb the subspace of all bounded elements in W. Finally, …

… Wilhelm Stannat, The theory of generalized Dirichlet forms and its applications in
analysis and stochastics, 1999 … If W is a subset of LP(E, m), let B, OW, B+ O. W and B: OW …

… Now we state the contraction theorem under the w-seminorm. … There exist nonnegative
constants c and w with 1 ≤ w < 1/α and a weight function w ≥ 1 such that ∀x ∈ X, (a) sup …

The ensemble Kalman filter has become a popular data assimilation technique in the
geosciences. However, little is known theoretically about its long term stability and accuracy. In this …

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles
of interacting neurons), we consider a population of mean field interacting diffusions in $\…

Let be a complete connected Riemannian manifold of dimension and let be a second order
elliptic operator on that has a representation in local coordinates, where, for some, and the …

… In this model, two variables, the voltage variable V having a cubic nonlinearity and a slower
recovery variable w describe the state of each neuron, that is reduced to one single point. …

… STANNAT … Recall that if U, W are Banach spaces, the Fréchet derivative of a function f :
U → W at u ∈ U is a linear mapping L : U → W such that …

… In (2.1), replacing W by a rough path W, we are interested in the following formal equation
… When replacing W by a rough path W, we are interested in the following equation …

… Röckner and W. Stannat, ‘Uniqueness of solutions of elliptic equations and uniqueness of
invariant … Stannat Fakultät für Mathematik Universität Bielefeld D–33501 Bielefeld Germany …