Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise
Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise
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DOI：
10.1016/j.spa.2020.06.007
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发表时间：
2018-10
影响因子：
1.4
通讯作者：
P. Chakraborty;Xia Chen;Bo Gao;S. Tindel
中科院分区：
文献类型：
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作者：
P. Chakraborty;Xia Chen;Bo Gao;S. Tindel
本文考虑一维抛物线型安德森模型，该模型在空间上具有与时间无关的分数阶噪声。考虑H< 12的情况，得到解的存在唯一性。为了找到解的猝灭渐近性，我们考虑了它的Feynman-Kac表示，并探讨了形式为1 2 Δ+ W ^ 0的随机算子的主特征值的渐近性。
In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise W ̇ in space. We consider the case H< 1 2 and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form 1 2 Δ+ W ̇.