Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.