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SUMMARY:Petr Čoupek (Department of Probability and Mathematical Statistic
 s\, Charles University)
DTSTART:20240514T113000Z
DTEND:20240514T123000Z
DTSTAMP:20260416T020715Z
UID:PHK-cohomology-seminar/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PHK-cohomolo
 gy-seminar/106/">Iterated integrals and controlled ODEs</a>\nby Petr Čoup
 ek (Department of Probability and Mathematical Statistics\, Charles Univer
 sity) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geo
 metry\, physics and statistics\n\n\nAbstract\nThe purpose of this non-tech
 nical talk is to discuss the role that\niterated integrals (an instance of
  the so-called mapping space signature)\nplay in the theory of ordinary di
 fferential equations (ODEs) of the form\n\n    \\[ \\dot{Y}(t) = f(Y(t))\\
 dot{X}(t)\\]\n\nwhere the path $X$ models the input and the path $Y$ model
 s the output\nof a physical system whose dynamics is governed by a (non-li
 near function)\n$f$. When $X$ is sufficiently regular (e.g.\\ Lipschitz) f
 unction\, the\nsolution to the ODE can be\, roughly speaking\, found as a 
 limit of its\niterated integrals. Such regularity is\, however\, typically
  not obtained\nif $X$ is a sample path of a stochastic process (e.g.\\ the
  Wiener process)\nand $\\dot X$ models the random noise (e.g.\\ the white 
 noise). In the talk\,\nwe will discuss why low regularity is a problem\, w
 hat can be done\, and why\nit is important to understand the algebraical a
 nd analytical properties of\nthe iterated integrals (and\, more generally\
 , the mapping space signature).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/106/
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