From Doob's maximal identity to Azema supermartingale

Published 14 Feb 2016 in math.PR | (1602.04480v2)

Abstract: We characterize the random times $\rho$ whose Azema supermartingales $Z^\rho$ take the form $Z^{\rho=U/U^*$} for some non negative local martingales $U$ starting from 1 vanishing at infinity, where $U^*$ denotes the running maximum process of $U$.

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Shiqi Song

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