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An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source
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We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an asymptotic theory for a wide class of non-linear SPDEs. A novel ingredient of this invariance principle is the dissipativity of the underlying stochastic PDE.
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On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation
The authors identify exact local and uniform spatio-temporal moduli of continuity for nonlinear parabolic SPDEs on bounded intervals and for the open KPZ equation, using new strong local non-determinism proofs under R...
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