Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

We present a novel framework for learning with sequential data of any kind, such as
multivariate time series, strings, or sequences of graphs. The main result is a" …

We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …

We develop the rough path counterpart of Itô stochastic integration and differential equations
driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) …

We build a hybrid theory of rough stochastic analysis which seamlessly combines the
advantages of both It\^ o's stochastic and Lyons' rough differential equations. This gives a …

We prove the pathwise well-posedness of stochastic porous media and fast diffusion
equations driven by nonlinear, conservative noise. As a consequence, the generation of a …

In this paper, we suggest approximate algorithms for the reconstruction of sparse high-
dimensional trigonometric polynomials, where the support in frequency domain is unknown …

We consider a framework for the construction of iterative schemes for operator equations
that combine low-rank approximation in tensor formats and adaptive approximation in a …

We discuss stochastic calculus for large classes of Gaussian processes, based on rough
path analysis. Our key condition is a covariance measure structure combined with a …