OPTIMAL STOPPING 387 2. Suppose that a(x)=0, b(x)= cos and 0.(x) 1. Then O'1(0) 0"2(0 1,/31(0) -/32(0)=1/2 and ;t_(z) z, and, therefore, by Remark the distribution of the random variable (0-0)4 Tconverges as T-m to the normal distribution with parameters (0, 2). Received by the editors February 18, 1974 REFERENCES [1] A. V. SKOROKHOD, Studies in the Theory of Random Processes, Addison-Wesley, Reading, Mass., 1965.[2] A. F. TARASKIN, On the asymptotic normality of vector stochastic integrals and the estimation of the drift parameters of a multi-dimensional diffusion process, Teor. Vet. Mat. Stat., 2 (1970), pp. 205-220. (In Russian.) [3] G. L. KULINICH, On the asymptotic behavior of the distributions offunctionals of a diffusion process of the type to g((s)) ds, Teor. Ver. Mat. Stat., 8 (1973), pp. 99-105. (In Russian.) [4] G. L. KULINICH, The asymptotic behavior of a non-stable solution of a homogeneous stochastic diffusion equation, Teor. Ver. Mat. Stat., 5 (1971), pp. 81-87. (In Russian.) [5] G. L. KULINICH, Limit distributions for integral-type functionals of non-stable diffusion processes, Teor. Ver. Mat. Stat., 11 (1974), pp. 81-85. (In Russian.) [6] G. L. KULINICH, On the limit behavior of the distribution of the solution of a stochastic diffusion equation, Theory Prob.Suppose a probability space (, , P) is given and on it a non-decreasing family of 0"-algebras t (s -, for s -< t, s _ ). A Markov diffusion process X is given on this probability space taking on values in d-dimensional Euclidean space E a and defined by the stochastic It6 equation $,x $,x X'X=x+ 0"(s+r,X, )dWr+ b(s+r, Xr )dr, t>0, s>0.Here W, is a d-dimensional Wiener process relative to ,, b(t, x) is a d-dimensional vector and 0"(t, x) is a d x d-matrix. The letter z will denote a Markov time with respect to the family {,}. Suppose also that T>0 is given and put Q={(t, x) :0_-