Renewal Theory
نویسنده
چکیده
(1) Sn = S0 + n ∑ i=1 Xi When S0 = 0 the renewal process is an ordinary renewal process; when S0 is a nonnegative random variable the renewal process is a delayed renewal process. In either case, the individual terms Sn of this sequence are called renewals, or sometimes occurrences. With each renewal process is associated a renewal counting process N (t ) that tracks the total number of renewals (not including the initial occurrence) to date: the random variable N (t ) is defined by N (t ) = max{n : Sn ≤ t } = τ(t )−1 where (2) τ(a) = min{n ≥ 1 : Sn > a}. (3)
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