Abstract
Let be a centered random walk with finite second moment. We consider the integrated random walk . We prove invariance principles for the meander and for the bridge of this process, under the condition that the integrated random walk remains positive. Furthermore, we prove the functional convergence of its Doob’s h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.
Acknowledgments
The authors would like to thank the anonymous referees, the Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Disclaimer. Michael Bär worked on this project in his personal capacity. Any opinions expressed in this article are his own and do not reflect the views of msg systems AG.
Citation
Michael Bär. Jetlir Duraj. Vitali Wachtel. "Invariance principles for integrated random walks conditioned to stay positive." Ann. Appl. Probab. 33 (1) 127 - 160, February 2023. https://doi.org/10.1214/22-AAP1811
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