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摘要
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) = -integral R-d K(y-x)[omega(dy) + W(dy)], where omega 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.
- 出版日期2013-10
- 单位吉林大学
