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THE BURGERS SUPERPROCESS Guillaume Bonnet a
 

Summary: THE BURGERS SUPERPROCESS
Guillaume Bonnet a
, Robert J. Adler b,1
aDepartment of Statistics and Applied Probability, UCSB
bFaculty of Industrial Engineering & Management, Technion, Israel
Abstract
We define the Burgers superprocess to be the solution of the stochastic partial
differential equation

t
u(t, x) = u(t, x) - u(t, x) u(t, x) + u(t, x) W(dt, dx),
where t 0, x R, and W is space-time white noise. Taking = 0 gives the classic
Burgers equation, an important, non-linear, partial differential equation. Taking
= 0 gives the super Brownian motion, an important, measure valued, stochastic
process. The combination gives a new process which can be viewed as a superprocess
with singular interactions. We prove the existence of a solution to this equation and
its H¨older continuity, and discuss (but cannot prove) uniqueness of the solution.
Key words: Burgers equation, superprocess, stochastic partial differential equation
PACS: 60H15, 60G57, Secondary 60H10, 60F05
1 The Burgers superprocess

  

Source: Adler, Robert J. - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology

 

Collections: Mathematics; Engineering