Strong Law of Large Numbers for a Class of Superdiffusions
In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of superdiffusions X corresponding to the evolution equation ? t u t =Lu t +?u t ??(u t ) on a domain of finite Lebesgue measure in ? d , where L is the generator of the underlying diffusion and the branching mechanism \(\psi(x,\lambda)=\frac{1}{2}\alpha(x)\lambda^{2}+\int_{0}^{\infty}(e^{-\lambda r}-1+\lambda r)n(x, \mathrm{d}r)\) satisfies \(\sup_{x\in D}\int_{0}^{\infty}(r\wedge r^{2}) n(x,\mathrm{d}r)<\infty\).
strong law of large numbers superdiffusion martingale point process principal eigenvalue 60j68 60g55 60g57