We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …

We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of
paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

We prove a general theorem on the stochastic convergence of appropriately renormalized
models arising from nonlinear stochastic PDEs. The theory of regularity structures gives a …

We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …

We show that the Markov semigroups generated by a large class of singular stochastic
PDEs satisfy the strong Feller property. These include for example the KPZ equation and the …

We are concerned with the three-dimensional incompressible Navier–Stokes equations
driven by an additive stochastic forcing of trace class. First, for every divergence free initial …

These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized
version of the three-dimensional stochastic nonlinear wave equation with quadratic …

We develop in this work a general version of paracontrolled calculus that allows to treat
analytically within this paradigm a whole class of singular partial differential equations with …