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

  • Spouge J
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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.

Author-supplied keywords

  • Excess over the boundary
  • Lorden's inequality
  • Renewal theory

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Authors

  • John L. Spouge

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