Sectorial convergence of U-statistics

Weak Convergence of Generalized U - Statistics

Convergence of U-statistics for interacting particle systems

The convergence of U -statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, dlPG99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the cor...

Asymptotics for the Moment Convergence of U-Statistics in LIL

A Remark on Convergence in Distribution of U-statistics

It is proved that, for h measurable and symmetric in its arguments and Xi i.i.d., if the sequence {n−m2 ∑ i1,...,im≤n ij 6=ik if j 6=k h(Xi1 ,...,Xim )}n=1, is stochastically bounded, then Eh2<∞ and Eh(X1,x2,...,xm)=0 a.s.

Convergence of Sectorial Operators on Varying Hilbert Spaces

Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on varying spaces is natural. However, it seems that the first results in this direction have been obtained only recently, to the best of our knowledge. Here we consider sectorial operators on scales of Hilbert spaces. We def...