Wick product in the stochastic Burgers equation: A curse or a cure?

Article type: Research Article

Authors: Kaligotla, S.^; | Lototsky, S.V.

Affiliations: Department of Mathematics, USC, Los Angeles, CA 90089, USA. E-mails: {kaligotl, lototsky}@usc.edu

Note: [] Corresponding author. E-mail: kaligotl@usc.edu.

Abstract: It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the renormalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burgers equation can only be interpreted in the Wick form, whence the cure. The analysis is based on the study of the coefficients of the chaos expansion of the solution at different stochastic scales.

Keywords: Catalan numbers, Hida–Kondratiev spaces, polynomial chaos

DOI: 10.3233/ASY-2011-1058

Journal: Asymptotic Analysis, vol. 75, no. 3-4, pp. 145-168, 2011