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Kyprianou, Maren Eckhoff, Matthias Winkel","submitted_at":"2013-09-24T14:58:16Z","abstract_excerpt":"Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism\n  -\\beta(x) z+\\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy).\n  The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. We use this decomposition to derive the Strong Law of Large Numbers (SLLN) for a wide class of superdiffusions from the corresponding result for branching particle diffusions. 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