6 papers
Signature Kernel and Schwinger-Dyson Kernel Equations as Two-Parameter Rough Differential Equations
Thomas Cass, Dan Crisan, Andrea Iannucci +1
We develop a rough-path framework for two-parameter rough differential equations on rectangular and simplicial domains, motivated by the signature kernel and Schwinger--Dyson kerne…
Random Controlled Differential Equations
Francesco Piatti, Thomas Cass, William F. Turner
We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly p…
Quantum Path Signatures
Samuel Crew, Cristopher Salvi, William F. Turner +2
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics…
Topologies on unparameterised rough path space
Thomas Cass, William F. Turner
The signature of a -weakly geometric rough path summarises a path up to a generalised notion of reparameterisation. The quotient space of equivalence classes on which the signat…
Free probability, path developments and signature kernels as universal scaling limits
Thomas Cass, William F. Turner
Random developments of a path into a matrix Lie group have recently been used to construct signature-based kernels on path space. Two examples include developments into GL$(N…
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…