Payoff sequence(x_n,?_n,n≥0)satisfy the stochastic difference equation x_n+1=x_n+a_n+b_nε_n+1，n=0,1,2,…, whereε_i,i=l, 2，…，is a white noise sequence. In this paper，we discussed the condition for Snell's envelope of(x_n, n≥0)to be approached by using Snell's envelope of finit sequence(x_n，0≤n≤N). We have obtained the decomposable representations of Snell's envelope of x_n=E(x_n︱?_n^ε)，n=0，1，2，…，where ?_n^ε=σ（ε_i，i=0,1,2,…,n）,ε₀=0. It is proposed that the necessary and sufficient condition for σ_n=inf (m≥n，r_m=X_m) is optimal stopping. At last，we discussed the iterative algorithm for optimal stopping rules and obtained the sufficient condition under which the iterative process can be stopped in finit steps.