Abstract
A general model of a branching random walk in Z is considered, where the branching and displacements occur with probabilities determined by the position of a parent. A necessary and sufficient condition is given for the random variable
to be finite. Here X n,k is the position of the k-th offspring in the n-th generation. The condition is stated in terms of a naturally arising linear functional equation. A number of examples are discussed, where the condition may be verified.
Ariclefootnote
This research was supported in part by the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 5545, USA, by Grant NM5E000 from the International Science Foundation and by the EC Grant ‘Human Capital and Mobility’, No 16296 (Contract CHRX-CT 93-0411).
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Karpelevich, F.I., Suhov, Y.M. (1997). A Criterion of Boundedness of Discrete Branching Random Walk. In: Athreya, K.B., Jagers, P. (eds) Classical and Modern Branching Processes. The IMA Volumes in Mathematics and its Applications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1862-3_10
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DOI: https://doi.org/10.1007/978-1-4612-1862-3_10
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