BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Nikolas Tapia (Weierstrass Institute)
DTSTART:20240209T140000Z
DTEND:20240209T150000Z
DTSTAMP:20260423T021605Z
UID:ACPMS/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/34/">B
 ranched Itô Formula and natural Itô-Stratonovich isomorphism</a>\nby Nik
 olas Tapia (Weierstrass Institute) as part of Algebraic and Combinatorial 
 Perspectives in the Mathematical Sciences\n\n\nAbstract\nBranched rough pa
 ths define integration theories that may fail to satisfy the integration b
 y parts identity. The projection of the Connes-Kreimer Hopf algebra (\\(\\
 mathcal{H}_{\\mathrm{CK}}\\)) onto its primitive elements defined by Broad
 hurst-Kreimer and Foissy\, allows us to view \\(\\mathcal{H}_{\\mathrm{CK}
 }\\) as a commutative \\(\\mathbf{B}_\\infty\\)-algebra and thus to write 
 an explicit change-of-variable formula for solutions to rough differential
  equations (RDEs)\, which restricts to the well-known Itô formula for sem
 imartingales. When compared with Kelly’s approach using bracket extensio
 ns\, this formula has the advantage of only depending on internal structur
 e. We proceed to define an isomorphism between \\(\\mathcal{H}_{\\mathrm{C
 K}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) (the shuffle algebra ove
 r primitives)\, which we compare with the previous constructions of Hairer
 -Kelly and Boedihardjo-Chevyrev: while all three allow one to write branch
 ed RDEs as RDEs driven by geometric rough paths taking values in a larger 
 space\, the key feature of our isomorphism is that it is natural when \\(\
 \mathcal{H}_{\\mathrm{CK}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) a
 re viewed as covariant functors \\(\\mathsf{Vec}\\to\\mathsf{Hopf}\\). Our
  natural isomorphism extends Hoffman’s exponential for the quasi shuffle
  algebra\, and in particular the usual Itô-Stratonovich correction formul
 a for semimartingales. Special emphasis is placed on the 1-dimensional cas
 e\, in which certain rough path terms can be expressed as polynomials in t
 he trace path indexed by \\(\\mathcal{P}\\)\, which for semimartingales re
 strict to the well-known Kailath-Segall polynomials.\n\nThis talk is based
  on joint work with E. Ferrucci and C. Bellingeri.\n
LOCATION:https://researchseminars.org/talk/ACPMS/34/
END:VEVENT
END:VCALENDAR