Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Hong, Jieliang"'
Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W=\{W(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. When $d\geq 3$, under the condition that th
Externí odkaz:
http://arxiv.org/abs/2406.06905
Autor:
Hong, Jieliang, Xiong, Jie
Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W^g=\{W^g(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. We show that when $d=1$, $X_t$ admits a
Externí odkaz:
http://arxiv.org/abs/2403.03638
Autor:
Hong, Jieliang, Mytnik, Leonid
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of $X_t$ is th
Externí odkaz:
http://arxiv.org/abs/2311.13757
Autor:
Hong, Jieliang
In dimensions $d\geq 4$, by choosing a suitable scaling parameter, we show that the rescaled spatial SIR epidemic process converges to a super-Brownian motion with drift, thus complementing the previous results by Lalley (Probab. Theory Related Field
Externí odkaz:
http://arxiv.org/abs/2309.08926
Autor:
Hong, Jieliang
For the range-R bond percolation in d=4,5,6, we obtain a lower bound for the critical probability p_c for R large, agreeing with the conjectured asymptotics and thus complementing the corresponding results of Van der Hofstad-Sakai (2005) for d>6, and
Externí odkaz:
http://arxiv.org/abs/2307.01466
Autor:
Hong, Jieliang, Mytnik, Leonid
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of $X_t$ is th
Externí odkaz:
http://arxiv.org/abs/2207.11705
Autor:
Hong, Jieliang
An upper bound for the critical probability of long range bond percolation in $d=2$ and $d=3$ is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins arXiv:arch-ive/160
Externí odkaz:
http://arxiv.org/abs/2107.14173
Autor:
Hong, Jieliang
If $L^x$ is the total occupation local time of $d$-dimensional super-Brownian motion, $X$, for $d=2$ and $d=3$, we construct a random measure $\mathcal{L}$, called the boundary local time measure, as a rescaling of $L^x e^{-\lambda L^x} dx$ as $\lamb
Externí odkaz:
http://arxiv.org/abs/2001.09137
Autor:
Hong, Jieliang
We use a renormalization of the total mass of the exit measure from the complement of a small ball centered at $x\in \mathbb{R}^d$ for $d\leq 3$ to give a new construction of the total local time $L^x$ of super-Brownian motion at $x$. In \cite{Hong20
Externí odkaz:
http://arxiv.org/abs/2001.07269
We show that if $\partial\mathcal{R}$ is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set $U$, $\partial\mathcal{R}\cap U\neq\emptyset$ implies $$\text{dim}(U\cap\part
Externí odkaz:
http://arxiv.org/abs/1809.04238