Some properties of the range of super-Brownian motion

Details Some properties of the range of super-Brownian motion Some properties of the range of super-Brownian motion

1998-06-22

arxiv.org/abs/math/9806120v1

Mathematics

Probability

Scientific paper

We consider a super-Brownian motion $X$. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the $\epsilon$-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of $X_t$ is capacity-equivalent to $[0,1]^2$ in $\R^d$, $d\geq 3$, and the range of $X$, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to $[0,1]^4$ in $\R^d$, $d\geq 5$.

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