Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?

Details Wick Product in The Stochastic Burgers Equation: A Curse or a Cure? Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?

2010-07-17

arxiv.org/abs/1007.2895v1

Mathematics

Probability

Scientific paper

It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, 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.

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