A general theorem for decomposition of linear random processes
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- by D. J. Hebert PDF
- Proc. Amer. Math. Soc. 38 (1973), 331-336 Request permission
Abstract:
Let $E$ and $F$ be locally convex spaces in duality and let $f$ be a linear random process indexed by $F$ such that the corresponding cylindrical measure is a Radon measure. It is shown without any assumptions of metrizability or countability that there is an equivalent process with continuous linear trajectories.References
- Albert Badrikian, Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques, Lecture Notes in Mathematics, Vol. 139, Springer-Verlag, Berlin-New York, 1970 (French). MR 0279271
- N. Bourbaki, Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaces topologiques séparés, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1343, Hermann, Paris, 1969 (French). MR 0276436
- A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York, Inc., New York, 1969. MR 0276438 L. Schwartz, Séminaire Laurent Schwartz—applications radonifiantes, École Polytechnique, Centre de Mathématiques, Paris, 1969/70.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 331-336
- MSC: Primary 28A40; Secondary 60G20
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320265-8
- MathSciNet review: 0320265