Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A general theorem for decomposition of linear random processes


Author: D. J. Hebert
Journal: Proc. Amer. Math. Soc. 38 (1973), 331-336
MSC: Primary 28A40; Secondary 60G20
MathSciNet review: 0320265
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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 (43 #4994)
  • [2] N. Bourbaki, Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaces topologiques séparés, Actualités Scientifiques et Industrielles, No. 1343, Hermann, Paris, 1969 (French). MR 0276436 (43 #2183)
  • [3] 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 (43 #2185)
  • [4] L. Schwartz, Séminaire Laurent Schwartz--applications radonifiantes, École Polytechnique, Centre de Mathématiques, Paris, 1969/70.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A40, 60G20

Retrieve articles in all journals with MSC: 28A40, 60G20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320265-8
PII: S 0002-9939(1973)0320265-8
Keywords: Generalized processes, cylindrical measures, lifting, decomposition
Article copyright: © Copyright 1973 American Mathematical Society