论文标题
lévy噪声中的连续性指向聚合物
The continuum directed polymer in Lévy Noise
论文作者
论文摘要
我们在本文中介绍了在时空lévy噪声给出的环境中的连续性指示聚合物模型的构建。该结构的主要目标之一是在重尾环境中描述离散的定向聚合物的缩放限制，因此，我们特别强调了$α$稳定的噪声，$α\ in（1,2）$。只要Lévy措施满足特定（和维度依赖）条件，我们的构造就可以在任意维度上进行。我们还讨论了连续聚合物的一些基本特性，以及该模型与随机热方程之间具有乘法lévy噪声的关系。
We present in this paper the construction of a continuum directed polymer model in an environment given by space-time Lévy noise. One of the main objectives of this construction is to describe the scaling limit of discrete directed polymer in an heavy-tail environment and for this reason we put special emphasis on the case of $α$-stable noises with $α\in (1,2)$. Our construction can be performed in arbitrary dimension, provided that the Lévy measure satisfies specific (and dimension dependent) conditions. We also discuss a few basic properties of the continuum polymer and the relation between this model and the Stochastic Heat Equation with multiplicative Lévy noise.
