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Unformatted text preview: E [ X t X s ] = E [ X t X s ] = R X ( s,t ) , and so we can write m m ( t ) = ZT 2T 2 m ( s ) R X ( t,s ) ds. Let us now resume our study of the correlation between X n and X m , which are coefcients of X ( ) according to the eigenfunction , E [ X m X n ] = E h h x, m i h x, n i i = E " ZT 2T 2 x ( s ) m ( s ) ds ZT 2T 2 x ( t ) n ( t ) dt # = ZT 2T 2 ZT 2T 2 m ( s ) E [ X s X t ] n ( t ) ds dt = ZT 2T 2 ZT 2T 2 m ( s ) R X ( s,t ) n ( t ) ds dt = ZT 2T 2 m m ( t ) n ( t ) dt = m ( mn ) . 1...
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 Fall '08
 Krim

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