Abstract
We study approximations to a class of vectorvalued equations of Burgers type driven by a multiplicative spacetime 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 ItôStratonovich correction in the theory of stochastic ordinary differential equations, where it is well known that different approximation schemes may converge to different solutions.
Original language  English 

Pages (fromto)  776870 
Number of pages  95 
Journal  Communications on Pure and Applied Mathematics 
Volume  67 
Issue number  5 
Early online date  2 Dec 2013 
DOIs  
Publication status  Published  1 May 2014 
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
Fingerprint Dive into the research topics of 'Approximating Rough Stochastic PDEs'. Together they form a unique fingerprint.
Profiles

Hendrik Weber
 Department of Mathematical Sciences  Professor of Probability
 Probability Laboratory at Bath
Person: Research & Teaching