00265 c44a3575504351098cf3798ec605dd
Statistical Process Monitoring with Integrated Moving Ayerage Noise 267
Markovian, X, 4_, is conditionally independent of Xł+U, given Xk. Thus, /(*)/** (Xk) = flk(Xlk )fkn (Xkn ) (3>
The corresponding equation, derived below, for h(-), the density of Y, implies that the elements of Y are Markovian.
Let
0<W =
where [•] denotes the greatest integer fiinction. As Ł ranges from 1 to 2"+,*0/(x)» generates all possible n-vectors with +xt or -xt in position /'. For
i<j let
v
For almost all yy we have
(4)
A*(y*)= Ź/«(e<(y*))
t=i
Using (3) and (4) and the symmetry of/gives the following string of eąualities which finishes the proof.
= 2Z/(e,(y))/«(^)
/=1
<=i
= ^(y.*K(yJ
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