On tail distributions of supremum and quadratic variation of local martingales

2005/03/04 by R. Liptser, Alexander Novikov, A. Novikov +2
Economics, Econometrics and Finance · Mathematics · #40E05 #60G44 #60HXX #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:40E05 #msc:60G44 #msc:60HXX

paper · pdf · doi:10.48550/arxiv.math/0503072

arxiv created 2005/03/04 · openalex publication_date 2005/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend some known results relating the distribution tails of a continuous local martingale supremum and its quadratic variation to the case of locally square integrable martingales with bounded jumps. The predictable and optional quadratic variations are involved in the main result.

Related

• Weak Tail Conditions for Local Martingales
• A Characterization Theorem for the Distribution of a Continuous Local Martingale and Related Limit Theorems
• Piecewise constant local martingales with bounded numbers of jumps
• Strict Local Martingales with Jumps
• Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps