Unfortunately, there's a little mistake in the thread.
Below is the correct
and the taylor expansion
Hey,
I've to show the following convergence.
,
,
whereas
is a standard Brownian motion
is a normal distributed random variable with continous paths
is a random variable with values in the interval , depends on and has continous paths
is a constant
is a constant
I started by using the taylor expansion of the exponential function for
and also the taylor expansion for the logarithm:
But how can I approximate the remainder term?
Can I change the order of the expectation value and the limit?
I know that
The following equation holds due to the definition of the Itô integral. Am I right?
where the limit is taken in
Does anybody have an idea how to show this convergence?
Can anybody help me?
Thanks!