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Invariance principles for integrated random walks conditioned to stay positive

Autor(en)
Bär, Michael ; Duraj, Jetlir ; Wachtel, Vitali
Zeitschrift
Annals of Applied Probability
Normierter Zeitschriftentitel
The annals of applied probability 
DOI
10.1214/22-AAP1811
ISSN
1050-5164
URL
https://pub.uni-bielefeld.de/record/2978105
Web of Science-ID
000946432400006

Weitere Details

Sprache
englisch
Darstellungsform
Text
Band
33
Ausgabe
1
Seitenbereich
127 - 160
Schlagwörter
Kolmogorov diffusion , Random walk harmonic function , h-transform , invariance principle

Let S (n) be a centered random walk with finite second moment. We con-sider the integrated random walk T (n) = S(0) + S(1) + center dot center dot center dot + S(n). We prove invariance principles for the meander and for the bridge of this process, un-der the condition that the integrated random walk remains positive. Further-more, we prove the functional convergence of its Doob's h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.

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