Additive-multiplicative stochastic warmth equations, stationary options, and Cauchy statistics
Authors: Alexander Dunlap, Chiranjib Mukherjee
Summary: We examine long-term habits and stationary distributions for stochastic warmth equations compelled concurrently by a multiplicative noise and an impartial additive noise with the identical distribution. We show that nontrivial space-time translation-invariant measures exist for all values of the parameters. We additionally present that if the multiplicative noise is sufficiently robust, the invariant measure has Cauchy-distributed marginals. Utilizing the identical methods, we show an analogous consequence on Cauchy-distributed marginals for a logarithmically attenuated model of the issue in two spatial dimensions. The proofs depend on stochastic evaluation and elementary potential principle.
