Publications [#384799] of Alexander J Dunlap

Papers Published

1. Dunlap, A; Mukherjee, C, Additive-multiplicative stochastic heat equations, stationary solutions, and Cauchy statistics, Annals of Applied Probability, vol. 35 no. 4 (August, 2025), pp. 2526-2543 [doi]
   (last updated on 2026/01/17)

   Abstract:
   We study long-term behavior and stationary distributions for stochastic heat equations forced simultaneously by a multiplicative noise and an independent additive noise with the same distribution. We prove that nontrivial space-time translation-invariant measures exist for all values of the parameters. We also show that if the multiplicative noise is sufficiently strong, the invariant measure has Cauchy-distributed marginals. Using the same techniques, we prove a similar result on Cauchy-distributed marginals for a logarithmically attenuated version of the problem in two spatial dimensions. The proofs rely on stochastic analysis and elementary potential theory.