An extension of Pratelli’s inequality

Adam Osękowski

Statistics & Probability Letters, 2021, vol. 177, issue C

Abstract: Let X, Y be càdlàg martingales and let Y# denote the sharp function of Y. The paper contains the proof of the estimate ‖∫0∞|d〈X,Y〉t|‖1≤2‖〈X〉1∕2Y#‖1 for the total variation between X and Y. The constant 2 is shown to be the best possible. The proof rests on the construction of an appropriate special function, enjoying certain size and concavity requirements.

Keywords: Martingale; Skew bracket; BMO; Sharp function; Best constant (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109175

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