 
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 spacetime white noise. Taking = 0 gives the classic
Burgers equation, an important, nonlinear, 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
