I am trying to solve a seemingly simple integral equation:
where is known to be zero for .
is a probability distribution function of a random process
where are iid random variables from a uniform distribution. I ran simulations of this process and got that is constant for and decays for . The decay does not seem to be exponential or 1/z. I did not manage to find an analytical solution or some transform (Laplace/Mellin) that can help.
Any suggestions would be welcome!