Can the stochastic wave equation with strong drift hit zero?
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DOI: 10.1214/19-ejp279
Abstract: We study the stochastic wave equation with multiplicative noise and singular drift: \[ \partial_tu(t,x)=\Delta u(t,x)+u^{-\alpha}(t,x)+g(u(t,x))\dot{W}(t,x) \] where $x$ lies in the circle $\mathbf{R}/J\mathbf{Z}$ and $u(0,x)>0$. We show that (i) If $0 read more here.
Keywords: stochastic wave; wave equation; drift; equation strong ... See more keywords