A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors

we consider the rounded-o€ value Xt ( n) ˆ n[Xt/ n We are interested in the asymptotic behaviour of the processes U(n, ')tˆ 1 2 1 i [nt]'(X ( n (iy 1)/n  p n(X ( n i/nyX(ty 1)/n ( n ) as n goes to ‡1: under suitable assumptions on ', and when the sequence n  p n goes to a limit 2 [0,1), we prove the convergence of U(n, ') to a limiting process in probability (for the local uniform topology), and an associated central