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journal article

A SPATIAL VERSION OF THE ITO-STRATONOVICH CORRECTION

Hairer, Martin  
•
Maas, Jan
July 1, 2012
ANNALS OF PROBABILITY

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 Ito Stratonovich correction term that arises when one considers different temporal discretizations of stochastic ODEs.

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Type
journal article
DOI
10.1214/11-AOP662
Web of Science ID

WOS:000306825000007

Author(s)
Hairer, Martin  
Maas, Jan
Date Issued

2012-07-01

Publisher

INST MATHEMATICAL STATISTICS

Published in
ANNALS OF PROBABILITY
Volume

40

Issue

4

Start page

1675

End page

1714

Subjects

STOCHASTIC BURGERS

•

EQUATIONS

•

Ito-Stratonovich correction

•

stochastic Burgers equation

•

spatial discretizations

•

Wiener chaos

•

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
PROPDE  
FunderFunding(s)Grant NumberGrant URL

EPSRC

EP/D071593/1, EP/E002269/1

Netherlands Organisation for Scientific Research (NWO)

680-50-0901

Philip Leverhulme prize of the Leverhulme Trust

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Available on Infoscience
September 17, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/241205
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