The separability of the Hilbert space generated by a stochastic process

J. Bulatovic and M. Asic

Journal of Multivariate Analysis, 1977, vol. 7, issue 1, 215-219

Abstract: The separability of the Hilbert space generated by a stochastic process is one of the basic assumptions in the time-spectral analysis of stochastic processes. This assumption is either presupposed explicitly or, more often, obtained as a consequence of the assumption of existence of left and right limits of the process for any value of the time parameter. In this paper it is shown that the existence of a left limit only, for each value of the time parameter, is a sufficient condition for the separability of the Hilbert space generated by the process.

Keywords: Stochastic; process; Hilbert; space; generated; by; a; stochastic; process; separability; left; and; right; limit (search for similar items in EconPapers)
Date: 1977
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