Advances in Applied Probability

Optimal online selection of an alternating subsequence: a central limit theorem

Alessandro Arlotto and J. Michael Steele

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Abstract

We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F, and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 2 (2014), 536-559.

Dates
First available in Project Euclid: 29 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1401369706

Digital Object Identifier
doi:10.1239/aap/1401369706

Mathematical Reviews number (MathSciNet)
MR3215545

Zentralblatt MATH identifier
1317.60011

Subjects
Primary: 60C05: Combinatorial probability 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 90C40: Markov and semi-Markov decision processes
Secondary: 60F05: Central limit and other weak theorems 90C27: Combinatorial optimization 90C39: Dynamic programming [See also 49L20]

Keywords
Bellman equation online selection Markov decision problem dynamic programming alternating subsequence central limit theorem nonhomogeneous Markov chain

Citation

Arlotto, Alessandro; Steele, J. Michael. Optimal online selection of an alternating subsequence: a central limit theorem. Adv. in Appl. Probab. 46 (2014), no. 2, 536--559. doi:10.1239/aap/1401369706. https://projecteuclid.org/euclid.aap/1401369706


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