Hey guys! I was working with with a couple of stochastic problems and found myself in a corner.
I have two Exponential processes (
respectively. Now suppose
. What is probability that
comes quicker than
I have reformulated this problem as follows: calculate
It appears I can calculate this, but now I have noticed that probably I should use conditional probability conditioning on the initial values (two conditions). If that's right how can I solve the problem? Could someone give me a hint?