Custom prior for gaussian process mean

Hi, I’m new to gaussian processes. I’m trying to model a process which I know that results in 0 near 0 input and goes to a positive constant at infinity.
Is there a way to set a suitable prior for this process? Optional solutions are:

  1. Using a step function for the prior, (0 below 0 and constant above).
  2. Using some nonlinear function such as y=1-exp(-x^4).

Is it possible to define such custom priors for the GP? It would make the extrapolation predictions much more reasonable.

Thank you.

Shortly after posting this question I found the following example which I think is very relevant:

However, there is a lot to learn there. I’ll try to go through it and if I make it, i’ll post here my conclusions.