Is the following sequence of integrable random variables also uniformly integrable?
is a standard Brownian motion,
is a random variable with values in [0,1],
is a standard-normal distributed random variable and is continous in
[0,T] is the time interval and it is required that and
is a constant
I also know that converges in probability for to a integrable random variable .
I've no idea how to show it.
Can anybody help me?
I found out that and converges in probability to this random variable
Can I now conclude that is uniformly integrable?