SOME PROPERTIES OF THE RANGE OF SUPER-BROWNIAN MOTION

JEAN-FRANÇOIS DELMAS

Abstract. 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 ε-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 ≥ 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 ≥ 5.