  In this paper we generalize the martingale of Kella and Whitt to the setting
of L\'{e}vy-type processes and show that the (local) martingales obtained are
in fact square integrable martingales which upon dividing by the time index
converge to zero a.s. and in $L^2$. The reflected L\'{e}vy-type process is
considered as an example.
