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

Prakash Chakraborty; Xia Chen; Bo Gao; Samy Tindel

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

Probability 2018-10-11 v1

Authors: Prakash Chakraborty , Xia Chen , Bo Gao , Samy Tindel

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 $\frac{1}{2} \Delta + \dot{W}$ .

Keywords

stochastic heat equation parabolic Anderson model fractional noise quenched asymptotics Feynman-Kac representation principal eigenvalue

Cite

@article{arxiv.1810.04212,
  title  = {Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise},
  author = {Prakash Chakraborty and Xia Chen and Bo Gao and Samy Tindel},
  journal= {arXiv preprint arXiv:1810.04212},
  year   = {2018}
}

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

Abstract

Keywords

Cite

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