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On the differentiability of the local time of the ()-stable super-Brownian motion
Ziyi Chen, Jieliang Hong
We consider the local times of -stable -dimensional super-Brownian motion with . Mytnik and Perkins (2003) proved that the local time, denoted by , is joi…
An upper bound for in range- bond percolation in two and three dimensions
Jieliang Hong
An upper bound for the critical probability of long range bond percolation in and is obtained by connecting the bond percolation with the SIR epidemic model, thus compl…
On the boundary local time measure of super-Brownian motion
Jieliang Hong
If is the total occupation local time of -dimensional super-Brownian motion, , for and , we construct a random measure , called the boundary loc…
Exit measure, local time and a boundary local time of super-Brownian motion
Jieliang Hong
We use a renormalization of the total mass of the exit measure from the complement of a small ball centered at for to give a new construction of the t…
On the topological boundary of the range of super-Brownian motion-extended version
Jieliang Hong, Leonid Mytnik, Edwin Perkins
We show that if is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set , $\…
Local behavior of local times of super Brownian motion
Jieliang Hong
For , in dimension , we study the asymptotic behavior of the local time of super-Brownian motion starting from as . Let $ψ(x)=((1/2…