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

Abstract

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 $\dot{W}$ is a white noise, $\psi \ge 0$ is smooth, compactly supported and non-trivial, and $0<p<1/2$. We further show that any solution spends positive time at the 0 function.

References in corpus (1)

• Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case

Cited by in corpus (1)

• Pathwise Uniqueness of the Solutions of Stochastic Heat Equation with Square-root Coefficient