A class of strong convergence theorem for an arbitrarily adapted stochastic sequence without the non-decrease condition was established by using the truncation method of stochastic variables and the stop time.

• 摘要引入了随机变量的截尾和停时的概念，在定理条件及其证明过程中适当地定义随机变量的截尾和停时，并通过定义鞅差序列和利用鞅差序列的收敛定理，得到了一类关于任意随机适应序列的强收敛定理。