The prolific backbone for supercritical superprocesses

We develop an idea of Evans and O’Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called ‘backbone’ decomposition for supercritical superprocesses. Our results also complement a related result for critical ( 1 + β ) -superprocesses given in Etheridge and Williams (2003) [11]. Our approach relies heavily on the use of Dynkin–Kuznetsov N -measures.