Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations

K. Burdzy, C. Mueller, E. A. Perkins

Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde $$\frac{\partial X}{\partial t}=\frac{\Delta }{2}X+X^p\dot{W}+\psi ,X_0\equiv 0$$ where $\dot…