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Parabolic Anderson Model with Rough Dependence in Space

  • Yaozhong HuEmail author
  • Jingyu Huang
  • Khoa Lê
  • David Nualart
  • Samy Tindel
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)

Abstract

This paper studies the one-dimensional parabolic Anderson model driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter \(H \in (\frac {1}{4}, \frac {1}{2})\) in the space variable. We derive the Wiener chaos expansion of the solution and a Feynman-Kac formula for the moments of the solution. These results allow us to establish sharp lower and upper asymptotic bounds for the nth moment of the solution.

Notes

Acknowledgements

We thank the referees for their useful comments which improved the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Yaozhong Hu
    • 1
    Email author
  • Jingyu Huang
    • 2
  • Khoa Lê
    • 3
  • David Nualart
    • 4
  • Samy Tindel
    • 5
  1. 1.Department of Mathematical and Statistical SciencesUniversity of Alberta at EdmontonEdmontonCanada
  2. 2.School of MathematicsUniversity of BirminghamBirminghamUK
  3. 3.Department of MathematicsImperial College LondonLondonUK
  4. 4.Department of MathematicsUniversity of KansasLawrenceUSA
  5. 5.Department of MathematicsPurdue UniversityWest LafayetteUSA

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