Stochastic processes are widely used for model building in the social, physical, engineering
and life sciences as well as in financial economics. In model building, statistical inference for …

This paper surveys in detail the relations between numerical integration and the Hamiltonian
(or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in …

While diffusion models have shown great success in image generation, their noise-inverting
generative process does not explicitly consider the structure of images, such as their …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

It is well-known that Control Theory was founded by N. Wiener in 1948 ([349]). After that, this
theory was greatly extended to various complicated setting and widely used in sciences and …

This book provides an introduction to the theory of stochastic partial differential equations
(SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability …

Artificial neural networks (ANNs) have very successfully been used in numerical simulations
for a series of computational problems ranging from image classification/image recognition …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

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 …