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 …

We introduce an approach to study certain singular partial differential equations (PDEs)
which is based on techniques from paradifferential calculus and on ideas from the theory of …

A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility.
First observed by Gatheral et al. in high‐frequency data, subsequently derived within market …

The sequence of moments of a vector-valued random variable can characterize its law. We
study the analogous problem for path-valued random variables, that is stochastic processes …

We define a characteristic function for probability measures on the signatures of geometric
rough paths. We determine sufficient conditions under which a random variable is uniquely …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …

The sequence of moments of a vector-valued random variable can characterize its law. We
study the analogous problem for path-valued random variables, that is stochastic processes …

We analyze common lifts of stochastic processes to rough paths/rough drivers-valued
processes and give sufficient conditions for the cocycle property to hold for these lifts. We …

Malliavin calculus is implemented in the context of Hairer (2014)[16]. This involves some
constructions of independent interest, notably an extension of the structure which …

In this article, we consider the so-called modified Euler scheme for stochastic differential
equations (SDEs) driven by fractional Brownian motions (fBm) with Hurst parameter ⅓< H< …