= i 11 Let 1 [0, 1] and define ti , for i = 0,1,2, ...,N and Tj = (1 - 1)t; + Atj+1, j = 0,1,...,N - 1. Find the explicit form of the following expression = N-1 Ki = N 700 tj+ KA = lim W.(W+1-Wt), j=0 where W7; and Wt; are Brownian motion processes and the limit is taken in the mean square sense. You may assume without proof that N-1 N-1 E N 700 lim E({(W; - W:) {(W1; Wt;)2 [(; t;) (CE 1) = 0. j=0 j=0 Hint: You may utilise the following identity: bc ba c2 ) (c 2 1 (2 a?) 360 a)2 + (6 a)2+(c b)(b a). 2 2 = i 11 Let 1 [0, 1] and define ti , for i = 0,1,2, ...,N and Tj = (1 - 1)t; + Atj+1, j = 0,1,...,N - 1. Find the explicit form of the following expression = N-1 Ki = N 700 tj+ KA = lim W.(W+1-Wt), j=0 where W7; and Wt; are Brownian motion processes and the limit is taken in the mean square sense. You may assume without proof that N-1 N-1 E N 700 lim E({(W; - W:) {(W1; Wt;)2 [(; t;) (CE 1) = 0. j=0 j=0 Hint: You may utilise the following identity: bc ba c2 ) (c 2 1 (2 a?) 360 a)2 + (6 a)2+(c b)(b a). 2 2