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DTSTAMP:20260425T075319Z
UID:1700496000@ist.ac.at
DTSTART:20231120T170000
DTEND:20231120T180000
DESCRIPTION:Speaker: Benjamin Robinson\nhosted by M. Beiglböck\, N. Berest
 ycki\, L. Erdös\, J. Maas\, F. Toninelli\, E. Schertzer\nAbstract: Given 
 a family of probability measures increasing in convex order\, does there e
 xist a Markov martingale with the corresponding marginal laws?  This que
 stion was answered positively by Strassen in 1965 in discrete time on a ge
 neral space\, and by Kellerer in 1972 in continuous time in dimension one.
  The multidimensional continuous-time case\, however\, remained open until
  recently.In this talk I present a multidimensional extension of Kellerer'
 s theorem. In particular I show that\, after applying some Gaussian regula
 rization to the given measures\, there exists a strongly Markovian marting
 ale Itô diffusion with these marginals. The proof of this result makes us
 e of the Bass martingales that arise in martingale optimal transport\, as 
 well as a mimicking theorem for Itô processes\, and a novel compactness r
 esult for martingale diffusions. In dimensions two and higher\, I show tha
 t uniqueness does not hold in general. In particular\, there exists a two-
 dimensional strong Markov martingale with continuous paths that has the sa
 me marginal laws as a Brownian motion and yet is not itself a Brownian mot
 ion. Moreover\, I present counterexamples showing that the existence of Ma
 rkov martingales with given marginal distributions may also fail in higher
  dimensions. Thus\, Kellerer's theorem cannot be extended to higher dimens
 ions in full generality. Joint work with Gudmund Pammer (ETH Zürich) and 
 Walter Schachermayer (Universität Wien).
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at 
SUMMARY:Benjamin Robinson: A regularized Kellerer theorem in arbitrary dime
 nsion
URL:https://talks-calendar.ista.ac.at/events/4605
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