Renewal theory

Common card · No. 377705

Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite expectation. A renewal-reward process additionally has a random sequence of rewards incurred at each holding time, which are IID but need not be independent of the holding times. A renewal process has asymptotic properties analogous to the strong law of large numbers and central limit theorem. The renewal function m ( t ) {\displaystyle m(t)} (expected number of arrivals) and reward function g ( t ) {\displaystyle g(t)} (expected reward value) are of key importance in renewal theory. The renewal function satisfies a recursive integral equation, the renewal equation. The key renewal...

Read on Wikipedia