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May 2019 Weak tail conditions for local martingales
Hardy Hulley, Johannes Ruf
Ann. Probab. 47(3): 1811-1825 (May 2019). DOI: 10.1214/18-AOP1302

Abstract

The following conditions are necessary and jointly sufficient for an arbitrary càdlàg local martingale to be a uniformly integrable martingale: (A) The weak tail of the supremum of its modulus is zero; (B) its jumps at the first-exit times from compact intervals converge to zero in $L^{1}$ on the events that those times are finite; and (C) its almost sure limit is an integrable random variable.

Citation

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Hardy Hulley. Johannes Ruf. "Weak tail conditions for local martingales." Ann. Probab. 47 (3) 1811 - 1825, May 2019. https://doi.org/10.1214/18-AOP1302

Information

Received: 1 January 2017; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067283
MathSciNet: MR3945760
Digital Object Identifier: 10.1214/18-AOP1302

Subjects:
Primary: 60G44

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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