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SUMMARY:Probability seminar: Peter Koepernik
DTSTART;TZID=Europe/London:20260622T150000
DTEND;TZID=Europe/London:20260622T160000
DTSTAMP:20260614T175451Z
UID:9e592f39-064e-f111-bec7-6045bdcfe41f
CREATED:20260512T132655Z
DESCRIPTION:Title: From $1/\\sqrt{n}$ to $1/n$: Accelerating SDE Simulatio
 n with Cubature Formulae\n\nAbstract: Monte Carlo sampling is the standard
  approach for estimating properties of solutions to stochastic differentia
 l equations (SDEs)\, but its error decays only as $1/\\sqrt{n}$\, requirin
 g huge sample sizes. Lyons and Victoir (2004) proposed replacing independe
 ntly sampled Brownian driving paths with "cubature formulae"\, determinist
 ic weighted sets of paths that match Brownian "signature moments" up to so
 me degree $D$. They prove that cubature formulae exist for arbitrary $D$\,
  but explicit constructions are difficult and have only reached $D=7$\, to
 o small for practical use.\n\nWe present an algorithm that efficiently and
  automatically constructs cubature formulae of arbitrary degree\, reproduc
 ing $D=7$ in seconds and reaching $D=19$ within hours on modest hardware. 
 In simulations across multiple SDEs\, our cubature formulae empirically ac
 hieve an error roughly of order $1/n$\, orders of magnitude smaller than M
 onte Carlo with the same number of paths.\n\nBased on joint work with Thom
 as Coxon and James Foster.
LAST-MODIFIED:20260512T132901Z
LOCATION:Woodstock Road - Mathematical Institute\, Mathematical Institute 
 Woodstock Road  Oxford Oxfordshire OX2 6GG United Kingdom
SPEAKER:Peter Koepernik (OpenAI)
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