Ito Integral in Equation (3.9) Let the interval 0 s t be partitioned into n subintervals, 0 = t1 < t2 < ...

Itˆo Integral in Equation (3.9) Let the interval 0 ≤ s ≤ t be partitioned into n subintervals, 0 = t1 < t2 < ... < tn+1 = t. For a Wiener process Wt assume Wt1 = 0.

a) Show n j=1 Wtj  Wtj+1 − Wtj  = 1 2 W2 t − 1 2 n j=1  Wtj+1 − Wtj 2

b) Use Lemma 1.9 to deduce Equation (3.9).