| | |
Summary: Cylindrical L´evy processes in Banach spaces
David Applebaum
Department of Probability and Statistics,
University of Sheffield,
Hicks Building, Hounsfield Road, Sheffield S3 7RH
United Kingdom.
Markus Riedle
School of Mathematics,
The University of Manchester,
Oxford Road,
Manchester M13 9PL
United Kingdom.
Abstract
Cylindrical probability measures are finitely additive measures on Banach spaces
that have sigma-additive projections to Euclidean spaces of all dimensions. They
are naturally associated to notions of weak (cylindrical) random variable and hence
weak (cylindrical) stochastic processes. In this paper we focus on cylindrical L´evy
processes. These have (weak) L´evy-It^o decompositions and an associated L´evy-
Khintchine formula. If the process is weakly square integrable, its covariance oper-
ator can be used to construct a reproducing kernel Hilbert space in which the process
|
