Initial measures for the stochastic heat equation
Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a family of nonlinear stochastic heat equations of the form , where denotes space–time white noise, the generator of a symmetric Lévy process on , and is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that for some , we prove that if is a finite measure of compact support, then the...