Inequalities on the overshoot beyond a boundary for independent summands with differing distributions

John L. Spouge

Statistics & Probability Letters, 2007, vol. 77, issue 14, 1486-1489

Abstract: Let {Sn:n[greater-or-equal, slanted]0} (S0=0) denote the successive sums of independent non-negative random variates, of possibly differing distributions. Define: (1) the number N(b)=inf{n[greater-or-equal, slanted]0:Sn>b} of sums in the interval [0,b]; and (2) the overshoot Rb=SN(b)-b. This paper bounds the tail and the moments .

Keywords: Renewal; theory; Excess; over; the; boundary; Lorden's; inequality (search for similar items in EconPapers)
Date: 2007
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