# Ito integral of an arbitrary f(Wiener process)

1. Jun 13, 2013

### saminator910

How would you take the Ito integral of an arbitrary $f(W_T)$ where $W_T$ is a standard Wiener process

$X_T=\int^t_0 f(W_s)dW_s$

would you somehow use Ito's lemma? I have attempted, but it doesn't seem to make sense...
$dX_T=f(W_T)dW_T$, There doesn't seem to be a $f(x)$ that makes sense for this in Ito's lemma.

$df = \frac{\partial f}{\partial x}dX_T + \frac{\partial^2 f}{\partial x^2}dX_T^2$

2. Jun 18, 2013

bump.....