Random walks are determined by their trace on the positive half-line
Annales Henri Lebesgue, Volume 3 (2020), pp. 1389-1397.


Keywords Random walk, Lévy process, Wiener–Hopf factorisation, Nevanlinna class


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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