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math.PR2026
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…
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…
math.PR2021
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…