Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations

Abstract

In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers the stochastic term in the Ito or Stratonovich sense. In particular, we prove that the Stratonovich interpretation may not produce modification in the exponential stability of the deterministic model for a wide range of stochastic perturbations, while Ito’s one can give different results. In fact, some stabilization or destabilization effect can be obtained.