solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看316次
Superdiffusions with large mass creation --- construction and growth estimates. (arXiv:1706.09864v1 [math.PR])
来源于:arXiv
Superdiffusions corresponding to differential operators of the form $\LL
u+\beta u-\alpha u^{2}$ with large mass creation term $\beta$ are studied. Our
construction for superdiffusions with large mass creations works for the
branching mechanism $\beta u-\alpha u^{1+\gamma},\ 0<\gamma<1,$ as well.
Let $D\subseteq\mathbb{R}^{d}$ be a domain in $\R^d$. When $\beta$ is large,
the generalized principal eigenvalue $\lambda_c$ of $L+\beta$ in $D$ is
typically infinite. Let $\{T_{t},t\ge0\}$ denote the Schr\"odinger semigroup of
$L+\beta$ in $D$ with zero Dirichlet boundary condition. Under the mild
assumption that there exists an $0<h\in C^{2}(D)$ so that $T_{t}h$ is
finite-valued for all $t\ge 0$, we show that there is a unique
$\mathcal{M}_{loc}(D)$-valued Markov process that satisfies a log-Laplace
equation in terms of the minimal nonnegative solution to a semilinear initial
value problem. Although for super-Brownian motion (SBM) this assumption
requires
$\beta$ be less than quadr 查看全文>>