Geodesic
On a structure of a conditioned random walk on the integers with bounded local times
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1265-1278

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We consider a sample path of a random walk on the integers with bounded local times, conditioned on the event that it hits a high level. Under an auxiliary assumption, we obtain representations for its distribution in terms of the corresponding limiting sequence. Then we prove limiting results as the high level grows. In particular, we generalize results for a simple symmetric random walk obtained earlier by Benjamini and Berectycki (2010).
Keywords: random walk, bounded local times, conditioned random walk, regenerative process, potential regeneration. 
@article{SEMR_2017_14_a51,
     author = {A. I. Sakhanenko and S. G. Foss},
     title = {On a structure of a conditioned random walk on the integers with bounded local times},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1265--1278},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a51/}
}
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A. I. Sakhanenko; S. G. Foss. On a structure of a conditioned random walk on the integers with bounded local times. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1265-1278. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a51/