A functional limit theorem for irregular SDEs

Stefan Ankirchner, Thomas Kruse, Mikhail Urusov

Let $X_1,X_2,\dots$ be a sequence of i.i.d. real-valued random variables with mean zero, and consider the scaled random walk of the form $Y^N_{k+1} = Y^N_{k} + a_N(Y^N_k) X_{k+1…