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SUMMARY:The Wasserstein space of stochastic processes
DTSTART;VALUE=DATE-TIME:20220803T153000Z
DTEND;VALUE=DATE-TIME:20220803T155000Z
DTSTAMP;VALUE=DATE-TIME:20231204T002015Z
UID:indico-contribution-1201@conference2.aau.at
DESCRIPTION:Researchers from different areas have independently defined ex
tensions of the usual weak topology between laws of stochastic processes.
This includes Aldous' extended weak convergence\, Hellwig's information t
opology and convergence in adapted distribution in the sense of Hoover-Kei
sler. We show that on the set of continuous processes with canonical filtr
ation these topologies coincide and are metrized by a suitable *adapted Wa
sserstein distance* $\\mathcal{AW}$. Moreover\, we show that the resulting
topology is the weakest topology that guarantees continuity of optimal st
opping. \n\nWhile the set of processes with natural filtration is not comp
lete\, we establish that its completion is precisely the space processes w
ith filtration $\\mathrm{FP}$. We also observe that $(\\mathrm{FP}\, \\mat
hcal{AW})$ exhibts several desirable properties. Specifically\, $(\\mathrm
{FP}\, \\mathcal{AW})$ is Polish\, martingales form a closed subset and ap
proximation results like Donsker's theorem extend to $\\mathcal{AW}$.\n\nT
his talk is based on joint work with Daniel Bartl\, Mathias BeiglbĂ¶ck\, G
udmund Pammer and Xin Zhang.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1201/
LOCATION:UniversitĂ¤t Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1201/
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