We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary “core” process that has a regenerative structure and plays a key role in our analysis. We obtain a number of representations for the distribution of the random walk in terms of the similar distribution of the “core” process. Based on that, we prove a number of limiting results by letting the high level to tend to infinity. In particular, we generalise results for a simple symmetric one-dimensional random walk obtained earlier in the paper by Benjamini and Berestycki (J Eur Math Soc 12(4):819–854, 2010).
|Title of host publication||In and Out of Equilibrium 3|
|Subtitle of host publication||Celebrating Vladas Sidoravicius|
|Editors||M. E. Vares, R. Fernández, L. R. Fontes , C. M. Newman |
|Number of pages||32|
|Publication status||Published - 2021|
|Name||Progress in Probability|