Abstract
Let X = X k k ⩾ 1 be an i.i.d. random sequence and Y = Y k k ⩾ 1 be an independent random sequence which is also independent of X. We suppose X and Y take values in the sequence space S N , where S is either N 0 , the space of non-negative integers, or R +, the space of non-negative numbers. Then X and X + Y = X k + Y k k ⩾ 1 induce probability measures μ X and μ X + Y on S N , respectively. We shall give necessary or sufficient conditions for μ X ∼ μ X + Y (equivalence = mutual absolute continuity) under assumptions on the distribution of X 1. In particular, we consider the case where X 1 obeys a Poisson or an exponential law.
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