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This article is cited in 23 scientific papers (total in 23 papers)
Skew Convolution Semigroups and Related Immigration Processes
Zeng-Hu Li Beijing Normal University
Abstract:
A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give a characterization for a general inhomogeneous skew convolution semigroup in terms of probability entrance laws. The related immigration process is constructed by summing up measure-valued paths in the Kuznetsov process determined by an entrance rule. The behavior of the Kuznetsov process is then studied, which provides insight into trajectory structures of the immigration process. Some well-known results on excessive measures are formulated in terms of stationary immigration processes.
Keywords:
measure-valued branching process, superprocess, immigration process, skew convolution semigroup, entrance law, entrance rule, excessive measure, Kuznetsov measure.
Received: 24.03.1999
Citation:
Zeng-Hu Li, “Skew Convolution Semigroups and Related Immigration Processes”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 247–274; Theory Probab. Appl., 46:2 (2002), 274–297
Linking options:
https://www.mathnet.ru/eng/tvp3917https://doi.org/10.4213/tvp3917 https://www.mathnet.ru/eng/tvp/v46/i2/p247
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