A.D.Wentzell (Tulane University) Limit theorems with asymptotic expansions for stochastic processes. There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expan-

There is a vast riches of limit theorems for sums of independent random variables: theorems about weak convergence, on large deviations, theorems with asymptotic expansions, etc. We can try to obtain the same kinds of theorems for families of stochastic processes. If X1, X2, ..., Xn, ... is a sequence of independent identically distributed random variables with expectation EXi = 0 and variance EX i = σ , everybody knows the theorem about weak convergence of the distribution of the random variable Zn = (X1+...+Xn)/ √ n: