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math.CA2024
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…
math.PR2024
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…