§ 1. The Conception of the Stochastic Dynamic Programming. In his recent study on the dynamic programming, Bellman [4] (p. 81) expresses the essence of the dynamic programming by the following five conditions, considering a system. a. In each case we have a (physical) system characterized at any stage by a small set of parameters, the state variables. b. At each stage of either process we have a choice of a number of decisions. c. The effect of a decision is a transformation of the state variables. d. The past history of the system is of no importance in determining future actions. e. The purpose of the process is to maximize some function of the state variables. The purpose of this work is to discuss some stochastic aspects of successive process of strategies in connection with the dynamic programming on the basis of the above f undamental concepts. In this section, let us consider the outline of our stochastic dynamic programming. At first, it is necessary to build a system. Let us build our system by the following notations.