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journal article

Approximating Rough Stochastic PDEs

Hairer, Martin  
•
Maas, Jan
•
Weber, Hendrik
May 1, 2014
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in Probability Theory Related Fields by Hairer and Weber. The key idea was to use the theory of controlled rough paths to give definitions of weak/mild solutions and to set up a Picard iteration argument.In this article the limiting behavior of a rather large class of (spatial) approximations to these equations is studied. These approximations are shown to converge and convergence rates are given, but the limit may depend on the particular choice of approximation. This effect is a spatial analogue to the Ito-Stratonovich correction in the theory of stochastic ordinary differential equations, where it is well known that different approximation schemes may converge to different solutions.(c) 2014 Wiley Periodicals, Inc.

  • Details
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Type
journal article
DOI
10.1002/cpa.21495
Web of Science ID

WOS:000332144200003

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

2014-05-01

Publisher

WILEY

Published in
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume

67

Issue

5

Start page

776

End page

870

Subjects

PARTIAL-DIFFERENTIAL-EQUATIONS

•

LATTICE APPROXIMATIONS

•

BURGERS

•

DRIVEN

•

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
PROPDE  
FunderFunding(s)Grant NumberGrant URL

EPSRC

EP/D071593/1

Leverhulme Trust through a Philip Leverhulme Prize

Netherlands Organisation for Scientific Research (NWO)

680-50-0901

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Available on Infoscience
September 17, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/241195
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