Mild solution to parabolic Anderson model in Gaussian and Poisson potential
Mild solution to parabolic Anderson model in Gaussian and Poisson potential
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DOI：
10.1063/1.4823860
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发表时间：
2013-10
影响因子：
1.3
通讯作者：
Yuecai Han;Liwei Zhang
中科院分区：
文献类型：
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作者：
Yuecai Han;Liwei Zhang
我们考虑由高斯和泊松随机介质共同生成的特殊随机齐次势中的抛物线安德森模型。在我们的模型中，系数 V(x) 不是具有正概率的 Holder 连续，因此该模型不太可能有路径解。我们为抛物线安德森模型构建了一个温和的解，其随机势为−V(x)=−∫RdK(y−x)[ω(dy)+W(dy)]，其中ω和W分别表示独立标准泊松点过程和中心高斯场。还处理电位符号切换且泊松场不存在的情况。
We consider the parabolic Anderson model in a special random homogeneous potential that is generated by the Gaussian and Poisson random medium together. In our model, the coefficient V(x) is not Holder continuous with positive probability, and thus the model is unlikely to have a path-wise solution. We construct a mild solution for the parabolic Anderson model with random potential of the form −V(x)=−∫RdK(y−x)[ω(dy)+W(dy)], where ω and W denote the independent standard Poisson point process and centred Gaussian field, respectively. The case where the potential switches in sign and the Poisson field is absent is handled as well.