A Singular Parabolic Anderson Model
نویسنده
چکیده
We consider the following stochastic partial differential equation: ∂u ∂t = 1 2 ∆u + κu ˙ F , for x ∈ R d in dimension d ≥ 3, where ˙ F (t, x) is a mean zero Gaussian noise with the singular covariance E ˙ F (t, x) ˙ F (t, y) = δ(t − s) |x − y| 2. Solutions u t (dx) exist as singular measures, under suitable assumptions on the initial conditions and for sufficiently small κ. We investigate various properties of the solutions using such tools as scaling, self-duality and moment formulae.
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