A NOTE ON THE MAXIMUM OF A RANDOM-WALK

Autor(en): STADJE, W 
Stichwörter: INTEGER-VALUED RANDOM WALK; Mathematics; MAXIMUM; MOMENT-GENERATING FUNCTION; Statistics & Probability
Erscheinungsdatum: 1995
Herausgeber: ELSEVIER SCIENCE BV
Journal: STATISTICS & PROBABILITY LETTERS
Volumen: 23
Ausgabe: 3
Startseite: 227
Seitenende: 231
Zusammenfassung: 
For an integer-valued, aperiodic random walk (S-n)(n greater than or equal to 1) with negative drift we consider its maximum M and M(+), its maximum before first attaining a nonpositive value. As a converse to well-known results on the asymptotic behavior of m(n) = P(M greater than or equal to n) and r(n) = P(M(+) greater than or equal to n), it is shown that any of the relations m(n) similar to cr(-n) or r(n) similar to cr(-n) (c > 1, r > 1) implies that E(r(S1)) = 1.
ISSN: 01677152
DOI: 10.1016/0167-7152(94)00117-Q

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