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We prove an invariance principle for the two-dimensional lattice parabolic Anderson model
with small potential. As applications we deduce a Donsker type convergence result for a …

An internal coproduct is described, which is compatible with Hoffman's quasi-shuffle product.
Hoffman's quasi-shuffle Hopf algebra, with deconcatenation coproduct, is a comodule-Hopf …

We apply Malliavin calculus to the Φ^4_3 equation on the torus and prove existence of
densities for the solution of the equation evaluated at regular enough test functions. We work …

We use the theory of regularity structures to develop an Itô formula for u, the solution of the
one-dimensional stochastic heat equation driven by space-time white noise with periodic …

Let T be the regularity structure associated with a given system of singular stochastic PDEs.
The paracontrolled representation of the Π map provides a linear parametrization of the …

We study a nonlinear parabolic stochastic partial differential equation (SPDE) with
multiplicative space–time white noise. The noise coecient is the square root of the unknown …

In this thesis we develop a general theory to prove the existence of several Itô formulae on
the one dimensional stochastic heat equation driven by additive space-time white noise …