RATES OF CONVERGENCE TO THE LOCAL TIME OF A DIFFUSION

In this paper we consider the approximation of the local time Lt of a I-dimensional diffusion process X at some level x, say x = 0 by normal ized sums, say U-t(n), of functions of the values X-i/n for i less tha n or equal to nt as n --> infinity. Our main aim is to prove an associ ated functional central limit theorem fiving a mixed normal limiting v alue to the sequence of processes n(infinity)(U-t(n) - L-t), for a sui table value of alpha. (C) Elsevier, Paris.