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Volume :23 Issue : 1 1996      Add To Cart                                                                    Download

Product processes in varying environments

Auther : MOKHTAR H. KONSOWA

 King Saud University, Al-Mulaidaa, Al Qasseem, P.O. Box 6033, Saudi Arabia

ABSTRACT

A particular type of branching process in varying environments is considered. It is assumed that all individuals of the same generation produce, given that the preceding generation is not extinct, randomly and independently of the past generations, the same number of children. We show that the number of children in the nth generation normed by its expectation converges almost surely to a limit whose expectation is 0 or 1. We give a sufficient condition for convergence in quadratic mean to a limit whose mean is one. A nonclassical norming sequence of constants is defined so that the almost sure limit is finite, greater than zero, with probability 1. We also show, under certain circumstances, that the almost sure limit has an infinite mean.

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