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

Wolfgang Stadje

Statistics & Probability Letters, 2000, vol. 50, issue 4, 375-381

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.

Keywords: Random; walk; Maximum; Approximation; Embedded; random; walk (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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