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Covariance factorisation and abstract representation of generalised random fields
- Source :
- Bulletin of the Australian Mathematical Society. 62:319-334
- Publication Year :
- 2000
- Publisher :
- Cambridge University Press (CUP), 2000.
-
Abstract
- This paper introduces a new concept of duality of generalised random fields using the geometric properties of Sobolev spaces of integer order. Under this duality condition, the covariance operators of a generalised random field and its dual can be factorised. The paper also defines a concept of generalised white noise relative to the geometries of the Sobolev spaces, and via the covariance factorisation, obtains a representation of the generalised random field as a stochastic equation driven by a generalised white noise. This representation is unique except for isometric isomorphisms on the parameter space.
Details
- ISSN :
- 17551633 and 00049727
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Australian Mathematical Society
- Accession number :
- edsair.doi...........99da2b07572c4462ad977dd2810f1b9a