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An iterative approximation procedure for the distribution of the maximum of a random walk

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  • Stadje, Wolfgang

Abstract

Let I(F) be the distribution function (d.f.) of the maximum of a random walk whose i.i.d. increments have the common d.f. F and a negative mean. We derive a recursive sequence of embedded random walks whose underlying d.f.'s Fk converge to the d.f. of the first ladder variable and satisfy F[greater-or-equal, slanted]F1[greater-or-equal, slanted]F2[greater-or-equal, slanted]... on [0,[infinity]) and I(F)=I(F1)=I(F2)=.... Using these random walks we obtain improved upper bounds for the difference of I(F) and the d.f. of the maximum of the random walk after finitely many steps.

Suggested Citation

  • Stadje, Wolfgang, 2000. "An iterative approximation procedure for the distribution of the maximum of a random walk," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 375-381, December.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:4:p:375-381
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    References listed on IDEAS

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    1. Stadje, Wolfgang, 1997. "A new approach to the Lindley recursion," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 169-175, January.
    2. Zhen Liu & Philippe Nain & Don Towsley, 1999. "Bounds for a class of stochastic recursive equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 325-333, April.
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    Cited by:

    1. Fotopoulos, Stergios B., 2009. "The geometric convergence rate of the classical change-point estimate," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 131-137, January.
    2. Alexander Novikov & Albert Shiryaev, 2004. "On an Effective Solution of the Optimal Stopping Problem for Random Walks," Research Paper Series 131, Quantitative Finance Research Centre, University of Technology, Sydney.

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