From Doob's maximal identity to Azema supermartingale

2016/02/14 by Shiqi Song, Song, Shiqi
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G07 #60G44 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G07 #msc:60G44

paper · pdf · doi:10.48550/arxiv.1602.04480

openalex publication_date 2016/02/14 · arxiv created 2016/02/28 · arxiv updated 2016/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the random times ρ whose Azema supermartingales Z^ρ take the form Z^ρ=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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