【摘要】 <正> 本文考虑定义在完备概率空间（Ω、（?）,P）上的生灭过程x（t,ω）,t≥0,ω∈Ω,其相空间为E=0,1,2,…,转移概率矩阵(P_ij（t）)（i,j∈E,t≥0）是标准的,并且其Q矩阵是更多还原

【Abstract】 An investigation has been made on the single-circulation birth and death proc-esses which are stationary and with constant probability currents called the circul-ations of the processes.The general formulae of the stationary probabitily distribution functions and the circulations of the processes are obtained here. It is found that when the bound-ary x∞ is exit, there will be one and only one single-circulation birth and death process which has a circulation value exactly equal to the reciprocal of R. When the boundary x∞ is extrance, there will be also one and only one such process which has a circulation value exactly equal to the reciprocal of S (if Q is non-conservative) or zero (if Q is conservation).It is also proved that for a non-conservative birth and death matrix, all non-terminating processes are ergodic and recurrent.更多还原