Abstract:
We study two-dimensional maxima of particle scores
in critical branching processes with immigration and
continuous time.
The limit distribution
for the maxima of two scores at two instants of time is found.
We obtain the limit intensities of upward and downward jumps of maxima
of one score and the limit intensities
of joint upward and downward jumps for both scores
or for at least one score.
In the case of independent scores,
we calculate the average numbers of joint upward and downward jumps of maxima
over the whole time period.
The results are illustrated with examples.
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