Is there a nice non-trivial example of a stopping time (discrete) whose distribution is geometric?
My original problem is to model a Bernoulli (or Poisson) process whose parameter is an adapted process. I did model something with the following steps: Define a Brownian motion and if it hits a threshold M, then the Bernolli process jumps to 1. However this does not give me a geometrically distributed jumps. In fact I am looking for a geometric distribution with stochastic probability of success.