Renewal theory for random variables with a heavy tailed distribution and finite variance
Geluk, Jaap J.L and Frenk , Hans J.B.G. (2011) Renewal theory for random variables with a heavy tailed distribution and finite variance. Statistics and Probability Letters, 81 (1). pp. 77-82. ISSN 0167-7152
This is the latest version of this item.
Official URL: http://dx.doi.org/10.1016/j.spl.2010.09.021
Let X-1, X-2,... X-n be independent and identically distributed (i.i.d.) non-negative random variables with a common distribution function (d.f.) F with unbounded support and EX12 < infinity. We show that for a large class of heavy tailed random variables with a finite variance the renewal function U satisfies U(x) - x/mu - mu(2)/2 mu(2) similar to -1/mu x integral(infinity)(x) integral(infinity)(s) (1 - F(u))duds as x -> infinity.
Available Versions of this Item
Repository Staff Only: item control page