A microlocal approach to renormalization in stochastic PDEs

We present a novel framework for the study of a large class of nonlinear stochastic partial differential equations (PDEs), which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedom without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic φd3 model.