4 papers
A Littlewood-Paley description of modelled distributions
Jörg Martin, Nicolas Perkowski
We exhibit a fundamental link between Hairer's theory of regularity structures and the paracontrolled calculus of Gubinelli, Imkeller and Perkowski. By using paraproducts we provid…
A regularity structure for rough volatility
Christian Bayer, Peter K. Friz, Paul Gassiat +2
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market…
Solution to the stochastic Schrödinger equation on the full space
Arnaud Debussche, Jörg Martin
We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schrödinger equation on can be enhanced to yield solutions on $\mathbb{R}^2…
Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model
Jörg Martin, Nicolas Perkowski
We develop a discrete version of paracontrolled distributions as a tool for deriving scaling limits of lattice systems, and we provide a formulation of paracontrolled distribution…