Levy white noise measures on infinite-dimensional spaces: Existence and characterization of the measurable support

摘要

It is shown that a Levy white noise measure A always exists as a Borel measure on the dual K' of the space K of C-infinity functions on R with compact support. Then a characterization theorem that ensures that the measurable support of Lambda is contained in S' is proved. In the course of the proofs, a representation of the Levy process as a function on K' is obtained and stochastic Levy integrals are studied. (C) 2006 Elsevier Inc. All rights reserved.