A Superprocess with coalescing spatial motion is constructed in terms of one-dimensional excursions. Based on this construction, it is proved that the superprocess is purely atomic and arises as scaling limit of a special form of the superprocess with dependent spatial motion studied in Dawson et al. (Refs. 5, 19-20).

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Keywords coalescing spatial motion, excursions, Poisson random measure, scaling limit, Superprocess
Persistent URL dx.doi.org/10.1023/B:JOTP.0000040293.67957.e3
Journal Journal of Theoretical Probability
Citation
Dawson, D.A, Li, Z., & Zhou, X. (2004). Superprocesses with coalescing Brownian spatial motion as large-scale limits. Journal of Theoretical Probability, 17(3), 673–692. doi:10.1023/B:JOTP.0000040293.67957.e3