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 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 …

In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of
rough differential equations (RDEs), notably drop** the assumption of continuity prevalent …

We provide in this work a robust solution theory for random rough differential equations of
mean field type dX_t=V\big(X_t,\mathcalL(X_t)\big)dt+F\bigl(X_t,\mathcalL(X_t)\bigr)dW_t …

We consider random walks and Lévy processes in a homogeneous group G. For all p> 0 p>
0, we completely characterise (almost) all G-valued Lévy processes whose sample paths …

We exhibit an explicit natural isomorphism between spaces of branched and geometric
rough paths. This provides a multi-level generalisation of the isomorphism of Lejay–Victoir …

We derive first-order Pontryagin optimality conditions for stochastic optimal control with
deterministic controls for systems modeled by rough differential equations (RDE) driven by …

These notes are an extended version of the course" Introduction to rough paths theory"
given at the XXV Brazilian School of Probability in Campinas in August 2022. Their aim is to …

We establish two results concerning a class of geometric rough paths X which arise as
Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support …

We give in this note a simple treatment of the non-explosion problem for rough differential
equations driven by unbounded vector fields and weak geometric rough paths of arbitrary …