Skew Convolution Semigroups and Related Immigration Processes

Details Skew Convolution Semigroups and Related Immigration Processes Skew Convolution Semigroups and Related Immigration Processes

2006-06-24

arxiv.org/abs/math/0606617v1

Theory of Probability and its Applications 46 (2002), 274-296

Mathematics

Probability

Scientific paper

A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give 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 insights into trajectory structures of the immigration process. Some well-known results on excessive measures are formulated in terms of stationary immigration processes.

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