Using the Chapman-Kolmogorov equation for the inference of discrete Random Walks

We address the problem of inferring the jump probabilities of a discrete Random Walk from the probability distribution of the process out equilibrium. We propose numerical methods and algorithms for solving this problem in 1 and 2 dimensions, based on the Chapman-Kolmogorov equation. The quantification of the a posteriori error of the calculated value is performed. Numerical experiments show the ability of the proposed computational procedure to infer the Random Walk parameters and the related accuracies.