Local approximations of Markov random walks by diffusions - Konakov, Valentin; Mammen, Enno (Stochastic processes and their applications, 2001)
We consider triangular arrays of Markov random walks that can be approximated by an accompanying sequence of diffusion processes. We give uniform bounds for approximation of scaled transition probabilities by transition densities of the diffusion process. In particular, we state local limit theorems for the case that the Markov random walks converge weakly to a diffusion process.
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