Abstract
We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial jump probabilities and show that such walks can be constructed so that P(Sun = 0) decays at polynomial rate n-α where α > 0 can be arbitrarily small. We also show, by means of a general delocalization lemma for martingales, which is of independent interest, that slower than polynomial decay is not possible.
Original language | English |
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Pages (from-to) | 1-8 |
Number of pages | 8 |
Journal | Electronic Communications in Probability |
Volume | 19 |
DOIs | |
State | Published - 18 Apr 2014 |
Keywords
- Martingale
- Random walk
- Stochastic control
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty