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

Autor(en): Stadje, W 
Stichwörter: approximation; embedded random walk; Mathematics; maximum; random walk; Statistics & Probability
Erscheinungsdatum: 2000
Herausgeber: ELSEVIER SCIENCE BV
Journal: STATISTICS & PROBABILITY LETTERS
Volumen: 50
Ausgabe: 4
Startseite: 375
Seitenende: 381
Zusammenfassung: 
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 than or equal to F-1 greater than or equal to F-2 greater than or equal to ... on [0, infinity) and I(F) = I(F-1) = I(F-2) = .... 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. (C) 2000 Elsevier Science B.V. All rights reserved.
ISSN: 01677152
DOI: 10.1016/S0167-7152(00)00124-3

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