Intermittency for the wave equation with L\'evy white noise
In this article, we consider the stochastic wave equation in dimension 1 driven by the L\'evy white noise introduced in Balan (2015). Using Rosenthal's inequality, we develop a maximal inequality for the moments of order $p \geq 2$ of the integral with respect to this noise. Based on this...
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Zusammenfassung: | In this article, we consider the stochastic wave equation in dimension 1
driven by the L\'evy white noise introduced in Balan (2015). Using Rosenthal's
inequality, we develop a maximal inequality for the moments of order $p \geq 2$
of the integral with respect to this noise. Based on this inequality, we show
that this equation has a unique solution, which is weakly intermittent in the
sense of Foondun and Khoshnevisan (2009) and Khoshnevisan (2014). |
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DOI: | 10.48550/arxiv.1505.04167 |