4. chen.dalang:15:moment

Moment bounds and asymptotics for the stochastic wave equation

Le Chen and Robert C. Dalang

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. system if and only if the initial state is integrable.

MSC 2010 subject classifications: Primary 60H15. Secondary 60G60, 35R60.

Keywords: nonlinear stochastic wave equation, hyperbolic Anderson model, intermittency, growth indices.

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[CD15a] Chen, Le & Dalang, Robert C. (2015) ‘Moment bounds and asymptotics for the stochastic wave equation’, Stochastic Process. Appl. 125, 1605–1628. <https://doi.org/10.1016/j.spa.2014.11.009>

@article{chen.dalang:15:moment,
  author        = {Chen, Le and Dalang, Robert C.},
  title         = {Moment bounds and asymptotics for the stochastic wave equation},
  journal       = {Stochastic Process. Appl.},
  fjournal      = {Stochastic Processes and their Applications},
  volume        = {125},
  year          = {2015},
  number        = {4},
  pages         = {1605--1628},
  issn          = {0304-4149},
  mrclass       = {60H15 (35R60 60G60)},
  mrnumber      = {3310358},
  mrreviewer    = {Martin Ondrej\'{a}t},
  doi           = {10.1016/j.spa.2014.11.009},
  url           = {https://doi.org/10.1016/j.spa.2014.11.009}
}

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