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Stochastic Dynamical Systems and Control |
| March 26, 2007 to March 30, 2007 |
| Organized By: Jonathan Mattingly (Duke), Igor Mezic (UCSB-Chair), Andrew Stuart (Warwick) |
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| Parent Programs: |
| Dynamical Systems |
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| Return to Workshop Description |
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On signed probability measures and some old work of Krylov
Friday March 30, 2007
10:30AM - 11:30AM
Speakers:
Terry Lyons
Abstract:
It is an interesting exercise to compute the iterated integrals of
Brownian Motion and to calculate the expectations (of polynomial
functions of these integrals).
Recent work on constructing discrete measures on path space, which give
the same value as Wiener measure to certain of these expectations, has
led to promising new numerical algorithms for solving 2nd order
parabolic PDEs in moderate dimensions. Old work of Krylov associated
finitely additive signed measures to certain constant coefficient PDEs
of higher order. Recent work with Levin allows us to identify the
relevant expectations of iterated integrals in this case, leaving many
interesting open questions and possible numerical algorithms for solving
high dimensional elliptic PDEs.
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