Asymptotics and Renewal Approximation in the Online Selection of Increasing Subsequence
Probability
2019-05-10 v2 Optimization and Control
Abstract
We revisit the problem of maximising the expected length of increasing subsequence that can be selected from a marked Poisson process by an online strategy. Resorting to a natural size variable, the problem is represented in terms of a controlled partially deterministic Markov process with decreasing paths. Refining known estimates we obtain fairly complete asymptotic expansions for the moments, and using a renewal approximation give a novel proof of the central limit theorem for the length of selected subsequence under the optimal strategy.
Keywords
Cite
@article{arxiv.1904.11213,
title = {Asymptotics and Renewal Approximation in the Online Selection of Increasing Subsequence},
author = {Alexander Gnedin and Amirlan Seksenbayev},
journal= {arXiv preprint arXiv:1904.11213},
year = {2019}
}
Comments
17 pages