Optimal On-Line Selection of an Alternating Subsequence: A Central Limit   Theorem
  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. 
Alessandro Arlotto and J. Michael Steele
math.PR math.OC