鞅型序列的另一类收敛定理

Let(x_n, f_n) be an integrable adapted sequence of r. v.'s, and , T the sets of all stopping times and bounded stopping times, respectively. In this paper we prove that (1) if (x_n,f_n) is a subpramart which satisfies the assumption (d_T~+): lim/T Ex_τ~+<∞ or (O~+): integral from n=(τ<∞)x_τ~+<∞, _τ∈, then (x_n) converges a. e.; (2) if (x_n,f_n) satisfies the assumption (O~+) or (d+): lim/n Ex_n~+<∞- and E(x_τ|f_n)—x_n]~-O(pr.),then (x_n) lower demiconverges a. e.,