Spectral multiplicity of some stochastic processes
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- by Slobodanka Mitrovic PDF
- Proc. Amer. Math. Soc. 126 (1998), 239-243 Request permission
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
- Harald Cramér, Structural and statistical problems for a class of stochastic processes, Princeton University Press, Princeton, N. J., 1971. The first Samuel Stanley Wilks lecture at Princeton University, Princeton, N. J., March 17, 1970; With an introduction by Frederick Mosteller. MR 0400370, DOI 10.1515/9781400885862
- —, Stochastic Processes as Curves in Hilbert Space, Theory Probab. Appl., Tom. 9 (1964), 193–204.
- Frédéric Riesz and Béla Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1972 (French); translated by the Amer. Math. Soc., 1974.
- T. N. Siraja, Canonical representations of second order random processes, Teor. Verojatnost. i Primenen. 22 (1977), no. 2, 429–435 (Russian, with English summary). MR 0451378
- Slobodanka Mitrović, A note concerning a theorem of Cramér, Proc. Amer. Math. Soc. 121 (1994), no. 2, 589–591. MR 1218117, DOI 10.1090/S0002-9939-1994-1218117-8
Additional Information
- Slobodanka Mitrovic
- Affiliation: Ljutice Bogdana 2/2 No. 35, Belgrade 11040, Serbia
- Email: emitrosl@ubbg.etf.bg.ac.yu
- 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 1998 American Mathematical Society
- 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