This article is cited 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

DOI: 10.4213/tvp3917

 English version: Theory of Probability and its Applications, 2002, 46:2, 274–297

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