Abstract
We derive integral representations for the renewal density u associated with a square integrable probability density p on [ 0 , ∞ ) having finite expected value μ. These representations express u in terms of the real and the imaginary part of the Fourier transform of p, considered as a function on the lower complex half plane. We use them to give simple global integrability conditions on p under which lim t → ∞ ( u ( t ) − p ( t ) ) = 1 / μ .
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