  In this work we present a modified neural network model which is capable to
simulate Markov Chains. We show how to express and train such a network, how to
ensure given statistical properties reflected in the training data and we
demonstrate several applications where the network produces non-deterministic
outcomes. One example is a random walker model, e.g. useful for simulation of
Brownian motions or a natural Tic-Tac-Toe network which ensures
non-deterministic game behavior.
