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SUMMARY:Signatures and functions on unparameterised path space - Thomas Ca
 ss (Imperial College London)
DTSTART:20220905T130000Z
DTEND:20220905T140000Z
UID:TALK178457@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:The signature is a non-commutative exponential that appeared i
 n the foundational work of K-T Chen in the 1950s. It is also a fundamental
  object in the theory of rough paths (Lyons\, 1998). More recently\, it ha
 s been proposed\, and used\, as part of a practical methodology to give a 
 way of summarising multimodal\, possibly irregularly sampled\, time-ordere
 d data in a way that is insensitive to its parameterisation. A key propert
 y underpinning this approach is the ability of linear functionals of the s
 ignature to approximate arbitrarily any compactly supported and continuous
  function on (unparameterised) path space. We present some new results on 
 the properties of a selection of topologies on the space of unparameterise
 d paths. Relatedly\, we review some recent innovations in the theory of th
 e signature kernel by introducing and analysing the properties of a family
  of so-called weighted signature kernels\n    The talk will draw on materi
 al from two recent papers\; one is joint work with William F. Turner\, the
  other is a joint work with Terry Lyons and Xingcheng Xu.
LOCATION:MR9\, Centre for Mathematical Sciences
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