Conditional Excursion Representation for a Class of Interacting Superprocesses
نویسندگان
چکیده
A class of interacting superprocesses, called superprocesses with dependent spatial motion (SDSMs), has been introduced and characterized in Wang [22] and Dawson et al. [7]. In this paper, we give a construction or an excursion representation of the non-degenerate SDSM with immigration by making use of a Poisson system associated with the conditional excursion laws of the SDSM. As pointed out in Wang [22], the multiplicative property or summable property is lost for SDSMs and immigration SDSMs. However, summable property is the foundation of excursion representation. This raises a sequence of technical difficulties. The main tool we used is the conditional log-Laplace functional technique that gives the conditional summability, the conditional excursion law, and the Poisson point process for the construction of the immigration SDSMs. AMS Subject Classifications: Primary 60J80, 60G57; Secondary 60J35
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