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

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Abstract

Let { Sn: n ≥ 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 ≥ 0 : Sn> b } of sums in the interval [0, b]; and (2) the overshoot Rb= SN (b)- b. This paper bounds the tail P { Rb> c } and the moments E Rbk.

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CITATION STYLE

APA

Spouge, J. L. (2007). Inequalities on the overshoot beyond a boundary for independent summands with differing distributions. Statistics and Probability Letters, 77(14), 1486–1489. https://doi.org/10.1016/j.spl.2007.02.013

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