论文标题
在无界域上布朗尼运动交点的大偏差原理
Large deviation principle for the intersection measure of Brownian motions on unbounded domains
论文作者
论文摘要
考虑交叉点测量$ \ ell^{\ mathrm {is}} _ t $ $ p $ p $独立的brownian motions on $ \ mathbb {r}^d $。在本文中，我们证明了归一化交叉点测量的大偏差原理$ t^{ - p} \ ell^{\ mathrm {is}} _ t $作为$ t \ rightArrow \ rightarrow \ infty $，然后退出（可能是没有绑定的）romain $ d \ subset $ d \ subset \ subset \ subset \ subset \ subset \ mathbb {r r Smpeque nourcy doumplese commise commise doumplese。这是[W. König和C. Mukherjee：关于纯和应用数学的通信，66（2）：263--306，2013]，涉及案例$ d $的情况。我们的基本贡献是通过应用查普曼 - 科尔莫格罗夫关系的应用，证明了所谓的超指定估算值对这种$ d $杀死的布朗尼动议的交叉措施。
Consider the intersection measure $\ell^{\mathrm{IS}}_t$ of $p$ independent Brownian motions on $\mathbb{R}^d$. In this article, we prove the large deviation principle for the normalized intersection measure $t^{-p}\ell^{\mathrm{IS}}_t$ as $t\rightarrow \infty$, before exiting a (possibly unbounded) domain $D\subset\mathbb{R}^d$ with smooth boundary. This is an extension of [W. König and C. Mukherjee: Communications on Pure and Applied Mathematics, 66(2):263--306, 2013] which deals with the case $D$ is bounded. Our essential contribution is to prove the so-called super-exponential estimate for the intersection measure of killed Brownian motions on such $D$ by an application of the Chapman-Kolmogorov relation.
