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Spectral multiplicity
of some stochastic processes


Author: Slobodanka Mitrovic
Journal: Proc. Amer. Math. Soc. 126 (1998), 239-243
MSC (1991): Primary 60G12
DOI: https://doi.org/10.1090/S0002-9939-98-04295-6
MathSciNet review: 1443396
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the connection between the canonical and the weak-canonical representations for the given second-order stochastic process in a separable Hilbert space and we extend a well-known theorem of H. Cramer concerning sufficient conditions for a process to be of multiplicity one.


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

  • 1. H. Cramer, Structural and Statistical Problems for a Class of Stochastic Processes, Princeton University Press, Princeton, New Jersey, 1971, pp. 30. MR 53:4204
  • 2. -, Stochastic Processes as Curves in Hilbert Space, Theory Probab. Appl., Tom. 9 (1964), 193-204.
  • 3. Frédéric Riesz and Béla Sz.-Nagy, Leçons d'analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1972 (French); translated by the Amer. Math. Soc., 1974.
  • 4. T. N. Siraja, Canonical representations of second order random processes, Teor. Veroyatnost. i Primenen. 12 (1977), 429-435. (Russian) MR 56:9664
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Additional Information

Slobodanka Mitrovic
Affiliation: Ljutice Bogdana 2/2 No. 35, Belgrade 11040, Serbia
Email: emitrosl@ubbg.etf.bg.ac.yu

DOI: https://doi.org/10.1090/S0002-9939-98-04295-6
Keywords: Second-order stochastic processes, canonical representation, spectral multiplicity
Received by editor(s): August 24, 1995
Additional Notes: This paper was presented at the 902nd AMS Meeting held at Burlington, Vermont, August 6–8, 1995
Communicated by: James Glimm
Article copyright: © Copyright 1998 American Mathematical Society

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