CRITERIA FOR THE UNIQUENESS OF HONEST Q-PROCESSES WITH FINITELY MRNY INSTANTANEOUS STATES

By the work of Williams³ and Hou⁴, we know that Q-processes are not unique when Q-matrix Q=(q_ij) contains instantaneous states. But honest Q-processes are not so. In fact, Chen⁵ has given an honest Q-matrix Q=(q_ij) with only one instantaneous state, whose honest Q-process is unique. Furthermore, in 8, Fei gave the criteria for the uniqueness of honest Q-processes with only one instantaneous state. This paper is an extension of the results in 8. We give the criteria for the uniqueness of honest Q-processes with finitely many instantaneous states.