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CATEGORIES:Probability
SUMMARY:Signatures and functions on unparameterised path s
pace - Thomas Cass (Imperial College London)
DTSTART;TZID=Europe/London:20220905T140000
DTEND;TZID=Europe/London:20220905T150000
UID:TALK178457AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178457
DESCRIPTION:The signature is a non-commutative exponential tha
t appeared in 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 recent
ly\, it has been proposed\, and used\, as part of
a practical methodology to give a way of summarisi
ng multimodal\, possibly irregularly sampled\, tim
e-ordered data in a way that is insensitive to its
parameterisation. A key property underpinning thi
s approach is the ability of linear functionals of
the signature to approximate arbitrarily any comp
actly supported and continuous function on (unpara
meterised) path space. We present some new results
on the properties of a selection of topologies on
the space of unparameterised paths. Relatedly\, w
e review some recent innovations in the theory of
the signature kernel by introducing and analysing
the properties of a family of so-called weighted s
ignature 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 wit
h Terry Lyons and Xingcheng Xu.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Jason Miller
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