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High Quality Content by WIKIPEDIA articles! Renewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times. Applications include calculating the expected time for a monkey who is randomly tapping at a keyboard to type the word Macbeth and comparing the long-term benefits of different insurance policies. A renewal process is a generalization of the Poisson process. In essence, the Poisson process is a continuous-time Markov process on the positive integers (usually starting at zero) which has independent identically distributed holding times at each integer i (exponentially distributed) before advancing (with probability 1) to the next integer:i + 1. In the same informal spirit, we may define a renewal process to be the same thing, except that the holding times take on a more general distribution. (Note however that the IID property of the holding times is retained).
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