Hitting times for the perturbed reflecting random walk
We consider a nearest neighbor random walk on Z which is reflecting at 0 and perturbed when it reaches its maximum. We compute the law of the hitting times and derive many corollaries, especially invariance principles with (rather) explicit descriptions of the asymptotic laws. We also obtain some results on the almost sure asymptotic behavior. As a by-product one can derive results on the reflecting Brownian motion perturbed at its maximum.
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Article provided by Elsevier in its journal Stochastic Processes and their Applications
Volume (Year): 123 (2013)Handle:
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Related researchKeywords: Perturbed random walk
; Once reinforced random walk
; Perturbed Brownian motion
; Hitting times
; Invariance principle
; Law of the iterated logarithm
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, click on "citations" and make appropriate adjustments.:
- Chaumont, L. & Doney, R. A., 2000.
"Some calculations for doubly perturbed Brownian motion,"
Stochastic Processes and their Applications,
Elsevier, vol. 85(1), pages 61-74, January.
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