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On a theorem on quasianalyticity of a weakly stationary process. (English) Zbl 0543.60046

It is shown that a regularity property, called quasianalyticity, of the covariance kernel of a measurable weakly stationary process X(t,\(\omega)\), \(t\in {\mathbb{R}}\), implies the existence of a modification \(X_ 0(t,\omega)\) of X(t,\(\omega)\) with almost surely quasianalytic sample paths. The problem originates from a paper by I. L. Ivanova, Teor. Funkts., Funkts. Anal. Prilozh. 5, 201-209 (1967; Zbl 0219.60033); English translation in Sel. Transl. Math. Stat. Probab. 12, 99-108 (1973).
Reviewer: H.Niemi

MSC:

60G17 Sample path properties
60G10 Stationary stochastic processes

Citations:

Zbl 0219.60033
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