聯絡我們 網站地圖 中央大學
 
 
   
     
 
主  題
KPZ equation, its renormalization and invariant measures  
 
 
 
時  間
2013-12-06 上午 10:00~12:00  
 
 
 
地  點
鴻經館 107 室  
 
 
 
主 講 者
Tadahisa Funaki (The University of Tokyo)  
 
 
 
內  容
Abstract:
The Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic partial differential equation, which is actually ill-posed because of inconsistency between the nonlinearity and the roughness of the noise. We introduce a renormalization procedure for the KPZ equation, which is appropriate from the view point to identify the invariant measures.

The Cole-Hopf transform applied to this approximating equation leads to a linear stochastic heat equation (SHE) with a smeared noise having an extra complex nonlinear term. Under the time average, this complex term can be replaced by a simple linear term, at least under the situation that the corresponding tilt process is stationary.

As a result, it is shown that the distribution of a two-sided geometric Brownian motion with a height shift given by Lebesgue measure is invariant under the evolution determined by the SHE.
 
   
 
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