2019/04/25 by Gnedin, Alexander, Seksenbayev, Amirlan
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)
paper · doi:10.48550/arxiv.1904.11213
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.