# How to use Neural Network to find a model which generate a given distribution?

For a non-Markovian random walk, each step can go up or down. And for the $$i_{th}$$ step, its step size $$S_i$$ may depend on the path of walk, and the probability for going up or down may also depend on the path of walk.

Let $$T_n = \sum_{i=1}^nS_i$$ be the displacement after a fixed number of steps $$n$$. Assuming the probability distribution: $$P(T_n=t)$$ will approach a given distribution.

Question: What kind of random walk (maybe with different step sizes, different step probability) can generate the given distribution in the limit (with some scale factors) ?

How can we use neural network to find such a random walk which can generate such expected distribution ?