An almost sure limit theorem for super-Brownian motion

Details An almost sure limit theorem for super-Brownian motion An almost sure limit theorem for super-Brownian motion

2008-12-03

arxiv.org/abs/0812.0642v1

Mathematics

Probability

14 pages

Scientific paper

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this case, the spectral theoretical assumptions that required in Chen et al (2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in $\mathbb{R}^d$.

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