Abstract
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).
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).
| Translated title of the contribution | On a structure of a conditioned random walk on the integers with bounded local times |
|---|---|
| Original language | Russian |
| Pages (from-to) | 1265-1278 |
| Number of pages | 14 |
| Journal | Siberian Electronic Mathematical Reports |
| Volume | 14 |
| DOIs | |
| Publication status | Published - 30 Nov 2017 |
Keywords
- random walk
- bounded local times
- potential regeneration
- regenerative process
- conditioned random walk