## Journal of Applied Probability

- J. Appl. Probab.
- Volume 48, Number 4 (2011), 1114-1132.

### Online selection of alternating subsequences from a random sample

Alessandro Arlotto, Robert W. Chen, Lawrence A. Shepp, and J. Michael Steele

#### Abstract

We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12 percent worse than a person who can make selections with full knowledge of the random sequence.

#### Article information

**Source**

J. Appl. Probab., Volume 48, Number 4 (2011), 1114-1132.

**Dates**

First available in Project Euclid: 16 December 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1324046022

**Digital Object Identifier**

doi:10.1239/jap/1324046022

**Mathematical Reviews number (MathSciNet)**

MR2896671

**Zentralblatt MATH identifier**

1258.90103

**Subjects**

Primary: 60C05: Combinatorial probability 90C40: Markov and semi-Markov decision processes

Secondary: 90C27: Combinatorial optimization 90C39: Dynamic programming [See also 49L20]

**Keywords**

Bellman equation online selection sequential selection prophet inequality alternating subsequence

#### Citation

Arlotto, Alessandro; Chen, Robert W.; Shepp, Lawrence A.; Steele, J. Michael. Online selection of alternating subsequences from a random sample. J. Appl. Probab. 48 (2011), no. 4, 1114--1132. doi:10.1239/jap/1324046022. https://projecteuclid.org/euclid.jap/1324046022