English

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}
}

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17 pages