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.