Summary
The objective of this paper is to investigate the structure of a general subcritical branching measure-valued processX subject to the usual regularity conditions. We prove that, if the second moments of the total massX t (E) are finite, thenX is a superprocess and we give an explicit expression of the branching characteristicsQ andl in terms of the continuous martingale component of the total massX t (E) and the Lévy measure (jumps compensator) ofX.
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Partially supported by National Science Foundation Grant DMS-9146347 and by The US Army Research Office through the Mathematical Sciences Institute at Cornell University