On the approximation of G-Diffusions by discrete-time G-Markov chains

In this paper, we introduce discrete-time G-Markov chains, which are families of sublinear expectations corresponding to Markov chains with uncertain transition probabilities. Our main result investigates the convergence to G-diffusions, which are extensions of Peng's G-expectation with a random G-function. More specifically, we establish convergence of the uncertainty sets in the Hausdorff metric topology as well as weak convergence of the corresponding sublinear expectations. This resembles a result from Stroock and Varadhan for the linear case without uncertainty. As an application, we discuss an approximation of Peng's G-expectation and some extensions.