Random walks are determined by their trace on the positive half-line

2019/02/22 by Kwaśnicki, Mateusz
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1902.08481

Abstract

We prove that the law of a random walk X_n is determined by the one-dimensional distributions of max(X_n, 0) for n = 1, 2, …, as conjectured recently by Loïc Chaumont and Ron Doney. Equivalently, the law of X_n is determined by its upward space-time Wiener-Hopf factor. Our methods are complex-analytic.

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