Symmetry of functions and exchangeability of random variables (2008)
Siburg, Karl Friedrich, Stoimenov, Pavel A.
We present a new approach for measuring the degree of exchangeability of two continuous, identically distributed random variables or, equivalently, the degree of symmetry of their corresponding...
Siburg, Karl Friedrich, Stoimenov, Pavel A.
We present a new way of constructing bivariate copulas, by rescaling and gluing two (or more) copulas. Examples illustrate how this construction can be applied to build complicated copulas from...
A scalar product for copulas (2007)
Siburg, Karl Friedrich, Stoimenov, Pavel A.
We introduce a scalar product for n-dimensional copulas, based on the Sobolev scalar product for W 1,2 -functions. The corresponding norm has quite remarkable properties and provides a new geometric...
A measure of mutual complete dependence (2007)
Siburg, Karl Friedrich, Stoimenov, Pavel A.
Two random variables X and Y are mutually completely dependent (m.c.d.) if there is a measurable bijection f with P(Y = f(X)) = 1. For continuous X and Y , a natural approach to constructing a...
The principle of least action in geometry and dynamics / Karl Friedrich Siburg (2004)
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Paternain, Gabriel P., Polterovich, Leonid, Siburg, Karl Friedrich
We consider Lagrangian submanifolds lying on a fiberwise strictly convex hypersurface in some cotangent bundle or, respectively, in the domain bounded by such a hypersurface. We establish a new...
On the asymptotic geometry of area-preserving maps (1999)
Polterovich, Leonid, Siburg, Karl Friedrich
We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the...
Symplectic capacities and bi-invariant metrics on Hamiltonian diffemorphisms [microform] / (1995)
Thesis (doctoral)--Eidgenössische Technische Hochschule Zürich, 1995.