Non-uniqueness for Non-negative Solutions of Parabolic Stochastic Partial Differential Equations
نویسنده
چکیده
Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde ∂X ∂t = ∆ 2 X +XẆ + ψ, X0 ≡ 0 where Ẇ is a white noise, ψ ≥ 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.
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