I am doing pricing of some financial instrument. I have simulated interest rate paths which follows the CIR process (see attached). Now, I want to find the probability of each part. This is under the assumption that we can treat each path as a state and inference a transition matrix P and a stationary distribution (pi(t)), s.t.

pi(t)*P = P

I would very much appreciate if any one with knowledge of these stochastic processes point me to a resource such as a paper, R or Python implementation code or any advice on how I could proceed.