  This paper presents with justifications a technique that is useful for the
study of piecewise deterministic Markov decision processes (PDMDPs) with
general policies and unbounded transition intensities. This technique produces
an auxiliary PDMDP from the original one. As to be discussed and claified, the
auxiliary PDMDP possesses certain desired properties, which may not be
possessed by the original PDMDP. Moreover, the performance measure of any
policy in the original PDMDP can be replicated by the auxiliary PDMDP for a
large class of performance criteria. As an application, we apply this technique
to risk-sensitive PDMDPs with total cost criteria.
