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Structural properties of a conditioned random walk on the integer lattice with local constraints
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Descriptif
We consider a random walk on a one/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 representations for the distribution of the random walk in terms of the similar distribution of the “core” process. Based on that, we prove limiting theorems 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 (2010).
The talk is based on a joint work with Alexander Sakhanenko.
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