Hi,

Having a random variable X I am trying to find a stochastic process Z_t such that:

P[Z_t > T] = P[X > T | X > t]

for all T>t, or a proof that such a process does not exist.

Please note that this question is not related to any homework and that I actually need this result for my research in financial maths.

Edit I haven't really mentioned it, but what I am really after is some sort of closed form formula for Z_t, ideally as a function of X and t.