Super-Brownian motion as the unique strong solution to an SPDE

Abstract

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.

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)

References in corpus (2)

• Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case
• Large Deviation Principle for Some Measure-Valued Processes

Cited by in corpus (4)

• Boundary behavior and interior Hölder regularity of solution to nonlinear stochastic partial differential equations driven by space-time white noise
• Backward doubly stochastic Volterra integral equations and applications to optimal control problems
• Well-posedness of martingale problem for SBM with interacting branching
• Backward doubly stochastic differential equations and SPDEs with quadratic growth