106 citations · 290 across the 24 of their papers we have counts for
27 papers
Generative Modelling of Lévy Area for High Order SDE Simulation
Andraž Jelinčič, Jiajie Tao, William F. Turner +3
It is well understood that, when numerically simulating SDEs with general noise, achieving a strong convergence rate better than (where h is the step size) requires t…
On the Wiener Chaos Expansion of the Signature of a Gaussian Process
Emilio Ferrucci, Thomas Cass
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H in (1/4, 1). At…
Topologies on unparameterised path space
Thomas Cass, William F. Turner
The signature of a path, introduced by K.T. Chen [5] in , has been extensively studied in recent years. The paper [12] of Hambly and Lyons showed that the signature is…
A combinatorial approach to geometric rough paths and their controlled paths
Thomas Cass, Bruce K. Driver, Christian Litterer +1
We develop the structure theory for transformations of weakly geometric rough paths of bounded -variation and their controlled paths. Our approach differs from existing appr…
Signature asymptotics, empirical processes, and optimal transport
Thomas Cass, William F. Turner, Remy Messadene
Rough path theory provides one with the notion of signature, a graded family of tensors which characterise, up to a negligible equivalence class, and ordered stream of vector-value…
General Signature Kernels
Thomas Cass, Terry Lyons, Xingcheng Xu
Suppose that and are two continuous bounded variation paths which take values in a finite-dimensional inner product space . Recent papers have introduced the truncated a…