Solve the following using the direct definition of the Ito Integral.

I(t) =

Z

t

0

udW(u) = lim

n

n1

X

i=0

n (t i )(W(t i+1 ) W(t i ))

By using the direct definition, I mean approximate the integrand with

the simple function n (u) evaluated over the partition of [0,t] given by

= {t 0 ,t 1 ,...,t n } and look at the limit. You may use Itos formula to

check your answer, but just using it to solve the integrand will result

in 0 points.

Salve the fellewing using the direct denitien ef the Ite Integral. t ul as: [a radius}: 11m assumesWan By using the direct denitien1 I mean appresimate the integrand with the simple fuuetien fujl evaluated ever the partition {if [Iii1 t] given by H = {t1}, t1, . . . ,tn} and leak at the limit. You ma},F use Itu's femula ta cheek yeur answer? but just using it tn salve the integrand will result in {l paints