Tytuł pozycji:
Renewal function asymptotics refined à la Feller
Feller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x → ∞, the renewal function U(x) of a renewal process with nonarithmetic generic lifetime X with finite mean E(X) = 1/λ and second moment differs from its linear asymptote λx by the quantity 1/2λ2E(X2). His first edition (1966) (but not the second in 1971) asserted that a similar approach would refine this asymptotic result when X has finite higher order moments. The paper shows how higher order moments may justify drawing conclusions from a recurrence relation that exploits a general renewal equation and further appeal to the Key Renewal Theorem.
Dedicated to Tomasz Rolski, a constant colleague over forty years, distance notwithstanding.
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
