If it helps, the vast majority of the details you provided are completely irrelevant. If I did it correctly, it is very easy to show . Just call the exponential term .
I've to find a constant such that for a random variable which is defined by
is a standard Brownian motion
is a normal distributed random variable
and are random variables with values in the interval
is a parameter
is a constant
Can anybody help me finding such that ?
Thanks a lot!!