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res:
bibo_abstract:
- We consider a class of stochastic PDEs of Burgers type in spatial dimension 1,
driven by space–time white noise. Even though it is well known that these equations
are well posed, it turns out that if one performs a spatial discretization of
the nonlinearity in the “wrong” way, then the sequence of approximate equations
does converge to a limit, but this limit exhibits an additional correction term.
This correction term is proportional to the local quadratic cross-variation (in
space) of the gradient of the conserved quantity with the solution itself. This
can be understood as a consequence of the fact that for any fixed time, the law
of the solution is locally equivalent to Wiener measure, where space plays the
role of time. In this sense, the correction term is similar to the usual Itô–Stratonovich
correction term that arises when one considers different temporal discretizations
of stochastic ODEs.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Martin
foaf_name: Hairer, Martin M
foaf_surname: Hairer
- foaf_Person:
foaf_givenName: Jan
foaf_name: Jan Maas
foaf_surname: Maas
foaf_workInfoHomepage: http://www.librecat.org/personId=4C5696CE-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-0845-1338
bibo_doi: 10.1214/11-AOP662
bibo_issue: '4'
bibo_volume: 40
dct_date: 2012^xs_gYear
dct_publisher: Institute of Mathematical Statistics@
dct_title: A spatial version of the Itô-Stratonovich correction@
...