TY - JOUR
T1 - Spectral densities describing off-white noises
AU - Tsirelson, Boris
PY - 2002
Y1 - 2002
N2 - For the white noise, the spectral density is constant, and the past (restriction to (-∞, 0)) is independent from the future (restriction to (0,+∞)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change. A necessary and sufficient condition for a spectral density to have such a property (in other words, to describe an off-white noise) is derived here from well-known results.
AB - For the white noise, the spectral density is constant, and the past (restriction to (-∞, 0)) is independent from the future (restriction to (0,+∞)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change. A necessary and sufficient condition for a spectral density to have such a property (in other words, to describe an off-white noise) is derived here from well-known results.
UR - http://www.scopus.com/inward/record.url?scp=0036845579&partnerID=8YFLogxK
U2 - 10.1016/S0246-0203(02)01133-0
DO - 10.1016/S0246-0203(02)01133-0
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AN - SCOPUS:0036845579
SN - 0246-0203
VL - 38
SP - 1059
EP - 1069
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
IS - 6
ER -