论文标题
随机谷物模型的非线性函数的缩放限制，并应用于汉堡方程
Scaling limits of nonlinear functions of random grain model, with application to Burgers' equation
论文作者
论文摘要
我们研究了非线性函数的缩放限制$ g $的随机谷物模型$ x $ on $ \ mathbb {r}^d $具有远距离依赖和边际泊松分布。继Kaj等人（2007年）之后，我们假设谷物基础泊松过程的强度$ m $与缩放参数$λ$一起增加，因为$ m =λ^γ$，对于某些$γ> 0 $。结果适用于布尔模型和指数$ g $，并依赖于$ g $ Charlier多项式的扩展以及Mehler的公式的概括。讨论了与初始聚合随机谷物数据的汉堡方程解决方程的应用。
We study scaling limits of nonlinear functions $G$ of random grain model $X$ on $\mathbb{R}^d $ with long-range dependence and marginal Poisson distribution. Following Kaj et al (2007) we assume that the intensity $M$ of the underlying Poisson process of grains increases together with the scaling parameter $λ$ as $M = λ^γ$, for some $γ> 0$. The results are applicable to the Boolean model and exponential $G$ and rely on an expansion of $G$ in Charlier polynomials and a generalization of Mehler's formula. Application to solution of Burgers' equation with initial aggregated random grain data is discussed.
