Strong law of large numbers for a class of superdiffusions

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Abstract: In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions

X

corresponding to the evolution equation

on a bounded domain

D

in

R^{d}

, where

L

is the generator of the underlying diffusion and the branching mechanism

p s i (x, l a m b d a) = 1 / 2 a l p h a (x) l a m b d a^{2} + i n t_{0}^{i} n f t y (e^{- l a m b d a r} - 1 + l a m b d a r) n (x, m d r)

satisfies

s u p_{x i n D} i n t_{0}^{i} n f t y (r w e d g e r^{2}) n (x, m d r) < i n f t y

.

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