A note on the maximum of a random walk
AbstractFor an integer-valued, aperiodic random walk (Sn)n [greater-or-equal, slanted] 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 mn = P(M [greater-or-equal, slanted] n) and rn = P(M+ [greater-or-equal, slanted] n), it is shown that any of the relations mn ~ cr-n or rn ~ cr-n (c > 1, r > 1) implies that E(rS1) = 1.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 23 (1995)
Issue (Month): 3 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Korshunov, D., 1997. "On distribution tail of the maximum of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 97-103, December.
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