lecture_32 (dragged) 3

lecture_32 (dragged) 3 - i th and j columns), so the...

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4 MA 36600 LECTURE NOTES: MONDAY, APRIL 13 When y k = x ( k ) we use the fact that x ° ip = ° j p ij ( t ) x jp to Fnd dW dt = ± σ ° ( σ ) d dt ² n ³ k =1 x ( k ) ´ = n ± i =1 ± σ ° ( σ ) dx ( i ) dt · ³ k ± = i x ( k ) = n ± i =1 n ± j =1 p ij ( t ) ± σ ° ( σ ) x ( i ) · ³ k ± = i x ( k ) = n ± i =1 n ± j =1 p ij ( t ) · W µ x (1) ,..., x ( i 1) , x ( j ) , x ( i +1) ,..., x ( n ) ( t ) . If j ° = i , then the expressions above involve matrices with two equal columns (namely the
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Unformatted text preview: i th and j columns), so the determinant is zero. Hence the sum reduces to the case where j = i : dW dt = n ± i =1 p ii ( t ) W = · tr P ( t ) ¸ W....
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.

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