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Spectral multiplicity of some stochastic processes

Author(s): Slobodanka Mitrovic
Journal: Proc. Amer. Math. Soc. 126 (1998), 239-243.
MSC (1991): Primary 60G12
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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:

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
5.: S. Mitrovic, A note concerning a theorem of Cramer, Proceedings of the Amer. Math. Soc., 121 (2) (1994), 589-591. MR 94h:60050

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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: 10.1090/S0002-9939-98-04295-6
PII: S 0002-9939(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
Copyright of article: Copyright 1998, American Mathematical Society


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