The Wold isomorphism for cyclostationary sequences

• In 1948 Wold introduced an isometric isomorphism between a Hilbert (linear) space formed from the weighted shifts of a numerical sequence and a suitable Hilbert space of values of a second-order stochastic sequence. Motivated by a recent resurrection of the idea in the context of cyclostationary sequences and processes, we present the details of the Wold isomorphism between cyclostationary stochastic sequences and cyclostationary numerical sequences. We show how Hilbert-space representations of cyclostationary sequences are interpreted in the case of numerical CS sequences.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

periodically correlated time series

Marcinkiewicz spaces

ergodic

properties

linear spaces generated by shifts of a sequence

time-series

linear-system

cumulant theory

probability

MATHEMATICS

Publication and Content Type

ref (subject category)

art (subject category)