Abstract
In this paper, we study the random sum SZn of independent and identically distributed (i.i.d.) random variables {Xi}, where {Zn} is a supercritical branching process in an i.i.d. environment ξ, and X1 is of zero mean and finite variance. We shall prove the large deviations of SZn, first in the case that Z1 has linear fractional distribution, then in some general case.
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