Subcritical superprocesses conditioned on non-extinction

We consider a class of subcritical superprocesses (Xt)t≥0 with general spatial motions and branching mechanisms. study the asymptotic behaviors Qt,r, distribution Xt conditioned on Xt+r not being null measure. first give existence limt→∞Qt,r limr→∞Qt,r, then show that an LlogL-type condition is equivalent to iterated limits: limr→∞limt→∞Qt,r limt→∞limr→∞Qt,r. Finally, when holds, we those limits, double limit limr,t→∞Qt,r, are same.