Additive-multiplicative stochastic heat equations, stationary choices, and Cauchy statistics
Authors: Alexander Dunlap, Chiranjib Mukherjee
Abstract: We study long-term habits and stationary distributions for stochastic heat equations compelled concurrently by a multiplicative noise and an neutral additive noise with the equivalent distribution. We present that nontrivial space-time translation-invariant measures exist for all values of the parameters. We moreover current that if the multiplicative noise is sufficiently strong, the invariant measure has Cauchy-distributed marginals. Using the equivalent strategies, we present a similar consequence on Cauchy-distributed marginals for a logarithmically attenuated mannequin of the difficulty in two spatial dimensions. The proofs rely on stochastic analysis and elementary potential precept.
