Consider, for example, the special case of G(t) = w(t). Then we find the expectation of 811 to be

i=l

i=l

" E(Sn] = L(t• - ti-l)a = (t-to)a. (41.3) i=l

Clearly, the value of 811 (and hence I), in this example, depends on a. For consistency, some specific choice must be made for the points {ri}·

J' G(s, w(s))dw(s) = ms-lim {t G(ti-ltw(ti-t))[w(ti)- w(ti-t))}, Jer n-oo .... i=l (41.4)

where ms-lim refers to the mean square limit.