  We consider a general piecewise deterministic Markov process (PDMP)
$X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for
which the conditional distribution function of the inter-occurrence time is not
necessarily absolutely continuous. A general form of the exponential
martingales is presented as
$$M^f_t=\frac{f(X_t)}{f(X_0)}\left[\mathrm{Sexp}\left(\int_{(0,t]}\frac{\mathrm{d}L(\mathcal{A}f)_s}{f(X_{s-})}\right)\right]^{-1}.$$
Using this exponential martingale as a likelihood ratio process, we define a
new probability measure. It is shown that the original process remains a
general PDMP under the new probability measure. And we find the new
measure-valued generator and its domain.
