On stopped decision processes with discrete time parameter

A non-stationary stopped decision process is investigated under rather weak convergence assumptions on the expected total rewards. Sufficient conditions are given for the approximation of the maximal conditional expected rewards from infinite stage play by the maximal conditional expected rewards from finite stage play. General criteria of optimality are derived. The results are essentially based on two lemmas given in this paper. The existence of optimal plans is established using results of non-stationary dynamic programming.