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Moment bounds and asymptotics for the stochastic wave equation

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  • Chen, Le
  • Dalang, Robert C.

Abstract

We consider the stochastic wave equation on the real line driven by space–time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to obtain sharp bounds on growth indices for certain classes of initial conditions with unbounded support.

Suggested Citation

  • Chen, Le & Dalang, Robert C., 2015. "Moment bounds and asymptotics for the stochastic wave equation," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1605-1628.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1605-1628
    DOI: 10.1016/j.spa.2014.11.009
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    References listed on IDEAS

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    1. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
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    Cited by:

    1. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.

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