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Radonification of cylindrical semimartingales on Hilbert spaces. (English) Zbl 0856.60005

It is shown that a cylindrical semi-martingale on a Hilbert space becomes a semi-martingale with values in that space when composed with three specific Hilbert-Schmidt operators.
Reviewer: A.Dale (Durban)

MSC:

60B05 Probability measures on topological spaces
60G99 Stochastic processes
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References:

[1] Badrikian, A. : Séminaire sur les Fonctions Aléatoires et les Mesures Cylindriques. vol.139. Springer, 1970. · Zbl 0209.48402
[2] Dellacherie, C. and Meyer, P.A.: Probabilités et Potentiel, Chapitre V-VIII. Paris, Hermann, 1980. · Zbl 0464.60001
[3] Memin, J.: “Espaces de semi-martingales et changement de probabilité”. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 52, p.9-39, 1980. · Zbl 0407.60046
[4] Schwartz, L.:“Semi-martingales banachiques: le théorème des trois opérateurs”. Séminaire de Probabilités XXVIII, p. 1- 20. vol. 1583. Springer, 1994. · Zbl 0812.60007
[5] Üstünel, A.S.:“A characterization of semimartingales on nuclear spaces”. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 60, p.21-39, 1982. · Zbl 0466.60006
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