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

2010/08/12 by K. Burdzy, C. Mueller, Burdzy, K. +3
Mathematics · #60H10 #60H40 #60J80 #60K35 #FOS: Mathematics #Primary 60H15. Secondary 60G60 #Probability (math.PR) #math.PR #msc:60G60 #msc:60H10 #msc:60H15. #msc:60H40 #msc:60J80 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1008.2126

arxiv created 2011/03/21 · arxiv updated 2011/03/23

Abstract

Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde (∂ X)/(∂ t)=\fracΔ2X+X^p W+ψ, X₀≡ 0 where W 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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