Abstract
Pathwise nonuniqueness is established for nonnegative solutions of the parabolic stochastic pde \[ \frac{\partial X}{\partial t}=\frac{\Delta}{2}X+X^p\dot W+\psi,\quad X_0 \equiv0 \] where $\dot W$ is a white noise, $\psi\ge0$ is smooth, compactly supported and nontrivial, and $0<p<1/2$. We further show that any solution spends positive time at the $0$ function.
Citation
K. Burdzy. C. Mueller. E. A. Perkins. "Nonuniqueness for nonnegative solutions of parabolic stochastic partial differential equations." Illinois J. Math. 54 (4) 1481 - 1507, Winter 2010. https://doi.org/10.1215/ijm/1348505538
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