Tove Nordmark: Finding the Maximum of a Sum of Two Random Walks with Fixed Endpoints

Abstract.

This text concerns the problem of finding the argument maximum of a sum of two random walks with fixed endpoints at 0, by choosing an appropriate subset of indices based on realizations of one of these walks. A measure of the effectiveness of a strategy for choosing such a set of indices has been proposed and a numerical study has been made. Furthermore, a subset asymptotically containing 1/4 of the indices which contains the argument maximum with probability 1 has been identified.