4,169 research outputs found
Super-Brownian motion as the unique strong solution to an SPDE
A stochastic partial differential equation (SPDE) is derived for
super-Brownian motion regarded as a distribution function valued process. The
strong uniqueness for the solution to this SPDE is obtained by an extended
Yamada-Watanabe argument. Similar results are also proved for the Fleming-Viot
process.Comment: Published in at http://dx.doi.org/10.1214/12-AOP789 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A stochastic log-Laplace equation
We study a nonlinear stochastic partial differential equation whose solution
is the conditional log-Laplace functional of a superprocess in a random
environment. We establish its existence and uniqueness by smoothing out the
nonlinear term and making use of the particle system representation developed
by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103-126].
We also derive the Wong-Zakai type approximation for this equation. As an
application, we give a direct proof of the moment formulas of Skoulakis and
Adler [Ann. Appl. Probab. 11 (2001) 488-543].Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000054
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