A NOTE ON THE CENTRAL-LIMIT-THEOREM FOR STOCHASTICALLY CONTINUOUS-PROCESSES

The desymmetrization technique which was successfully used in C(S) spaces is carried over to limit theorems for stochastically continuous random processes with sample paths in Skorohod space D[0,1] and is applied to obtain the central limit theorem (CLT) in D[0,1]. Let {X(t), t is an element of [0,1]} be a stochastically continuous random process. For functions f, g such that E(\X(s) - X(t)\ boolean AND \X(t) - X(u)\)(p) less than or equal to f(u - s), E\X(s) - X(t)\(q) less than or equal to g(t - s), p, q greater than or equal to 2, s less than or equal to t less than or equal to u, conditions are found which imply the CLT in D[0.1].