55 citations · 97 across the 13 of their papers we have counts for
13 papers
Exact dimension reduction for rough differential equations
Martin Redmann, Sebastian Riedel
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated.…
Introduction to rough paths theory
Mazyar Ghani Varzaneh, Sebastian Riedel
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…
The geometry of controlled rough paths
Mazyar Ghani Varzaneh, Sebastian Riedel, Alexander Schmeding +1
We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dime…
A Wong-Zakai theorem for SDEs with singular drift
Chengcheng Ling, Sebastian Riedel, Michael Scheutzow
We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the form w…
Semi-implicit Taylor schemes for stiff rough differential equations
Sebastian Riedel, Yue Wu
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a gene…
A dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds
Mazyar Ghani Varzaneh, Sebastian Riedel
Building on results obtained in [GVRS], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rou…
A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces
Mazyar Ghani Varzaneh, Sebastian Riedel, Michael Scheutzow
We show that singular stochastic delay differential equations (SDDEs) induce cocycle maps on a field of Banach spaces. A general Multiplicative Ergodic Theorem on fields of Banach…
Random dynamical systems, rough paths and rough flows
Ismael Bailleul, Sebastian Riedel, Michael Scheutzow
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 sh…
The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
Peter K. Friz, Benjamin Gess, Archil Gulisashvili +1
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 classical…
From rough path estimates to multilevel Monte Carlo
Christian Bayer, Peter K. Friz, Sebastian Riedel +1
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a…
Spatial rough path lifts of stochastic convolutions
Peter K. Friz, Benjamin Gess, Archil Gulisashvili +1
We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their va…
A simple proof of distance bounds for Gaussian rough paths
Sebastian Riedel, Weijun Xu
We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assum…
Integrability of (non-)linear rough differential equations and integrals
Peter Friz, Sebastian Riedel
Integrability properties of (classical, linear, linear growth) rough differential equations (RDEs) are considered, the Jacobian of the RDE flow driven by Gaussian signals being a m…