Inequalities on the Overshoot beyond a Boundary for Independent Summands with Differing Distributions.
Let {S(n) : n >/= 0} (S(0) = 0) denote the successive sums of independent non-negative random variates, of possibly differing distributions. Define: (1) the number N(b) = inf{n >/= 0 : S(n) > b} of sums in the interval [0,b]; and (2) the overshoot R(b) = S(N(b)) -b. This paper bounds the tail P{R(b) > c} and the moments Rbk.
Spouge
John L
JL
National Center for Biotechnology Information National Library of Medicine.