PATHWISE NONUNIQUENESS FOR THE SPDES OF SOME SUPER-BROWNIAN MOTIONS WITH IMMIGRATION

• 成果类型: Article
• 署名作者: Chen, Yu-Ting
• 署名单位: Harvard University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP962
• 发表日期: 2015
• 页码: 3359-3467
• 关键词: partial-differential equations; uniqueness

摘要

We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In contrast to a closely related case investigated by Mueller, Mytnik and Perkins [Ann. Probab. 42 (2014) 2032-21121, the solutions of the present SPDEs are assumed to be nonnegative and have very different properties including uniqueness in law. In proving possible separation of solutions, we derive delicate properties of certain correlated approximating solutions, which is based on a novel coupling method called continuous decomposition. In general, this method may be of independent interest in furnishing solutions of SPDEs with intrinsic adapted structure.