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Propagation of singularities for the stochastic wave equation

Author

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  • Lee, Cheuk Yin
  • Xiao, Yimin

Abstract

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the iterated logarithm and general methods for Gaussian processes.

Suggested Citation

  • Lee, Cheuk Yin & Xiao, Yimin, 2022. "Propagation of singularities for the stochastic wave equation," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 31-54.
    • Handle: RePEc:eee:spapps:v:143:y:2022:i:c:p:31-54
    DOI: 10.1016/j.spa.2021.09.013
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    References listed on IDEAS

    as
    1. Ortega, Joaquín, 1984. "On the size of the increments of nonstationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 47-56, September.
    2. Blath, Jochen & Martin, Andreas, 2008. "Propagation of singularities in the semi-fractional Brownian sheet," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1264-1277, July.
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