Superprocesses of stochastic flows

• 成果类型: Article
• 署名作者: Ma, ZM; Xiang, KN
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University; Universidade de Lisboa
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 317-343
• 关键词: brownian motions; SPACE

摘要

We construct a continuous superprocess X on M(Rd) which is the unique weak Feller extension of the empirical process of consistent k-point motions generated by a family of differential operators. The process X differs from known Dawson-Watanabe type, Fleming-Viot type and Ornstein-Uhlenbeck type superprocesses. This new type of superprocess provides a connection between stochastic flows and measure-valued processes, and determines a stochastic coalescence which is similar to those of Smoluchowski. Moreover, the support of X describes how an initial measure on Rd is transported under the flow. As an example, the process realizes a viewpoint of Darling about the isotropic stochastic flows under certain conditions.