arXiv subjects

S. Geiss

Publications and source records attributed to S. Geiss.

2 recordsLinked to original sources

arXiv2014

Permutation Invariant Functionals of L\'evy Processes

We study natural invariance properties of functionals defined on L\'evy processes and show that they can be described by a simplified structure of the deterministic chaos kernels in It\^o's chaos expansion. These structural properties of the kernels relate intrinsically to a measurability with respect to invariant $\sigma$-algebras. This makes it possible to apply deterministic functions to invariant functionals on L\'evy processes while keeping the simplified structure of the kernels. This stability is crucial for applications. Examples are given as well.

math.PR↗

arXiv2008

On singular integral and martingale transforms

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.

math.CA↗