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

Author

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  • Chakraborty, Prakash
  • Chen, Xia
  • Gao, Bo
  • Tindel, Samy

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.

Suggested Citation

  • Chakraborty, Prakash & Chen, Xia & Gao, Bo & Tindel, Samy, 2020. "Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6689-6732.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6689-6732
    DOI: 10.1016/j.spa.2020.06.007
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