  This paper gives a complete characterization of infinitely divisible
semimartingales, i.e., semimartingales whose finite dimensional distributions
are infinitely divisible. An explicit and essentially unique decomposition of
such semimartingales is obtained. A new approach, combining series
decompositions of infinitely divisible processes with detailed analysis of
their jumps, is presented. As an ilustration of the main result, the
semimartingale property is explicitely determined for a large class of
stationary increment processes and several examples of processes of interest
are considered. These results extend Stricker's theorem characterizing Gaussian
semimartingales and Knight's theorem describing Gaussian moving average
semimartingales, in particular.
