Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

Prakash Chakraborty; Xia Chen; Bo Gao; Samy Tindel

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arXiv · 1810.04212

Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

Prakash Chakraborty·Xia Chen·Bo Gao·Samy Tindel

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Abstract

In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $\dot{W}$ in space. We consider the case $H<\frac{1}{2}$ 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 $\frac{1}{2} \Delta + \dot{W}$.

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Prakash Chakraborty, Xia Chen, Bo Gao, Samy Tindel. 2018-10-09. Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise. https://arxiv.org/abs/1810.04212

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