Limits of random walks with distributionally robust transition probabilities

We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within neighborhood (w.r.t. Wasserstein distance) of the fixed Lévy process. In analogy classical framework we show that, when passing from discrete continuous via scaling limit, this gives rise semigroup. explicitly compute generator semigroup and corresponding PDE as perturbation initial