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

Prakash Chakraborty, Xia Chen, Bo Gao and Samy Tindel

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6689-6732

Abstract: In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case H<12 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 12Δ+Ẇ.

Keywords: Stochastic heat equation; Parabolic Anderson model; Fractional Brownian motion; Feynman–Kac formula; Lyapounov exponent (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.06.007

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