Weak tail conditions for local martingales
Hulley, H. & Ruf, J.
(2019).
Weak tail conditions for local martingales.
Annals of Probability,
47(3), 1811-1825.
https://doi.org/10.1214/18-AOP1302
(2019).
Weak tail conditions for local martingales.
Annals of Probability,
47(3), 1811-1825.
https://doi.org/10.1214/18-AOP1302
The following conditions are necessary and jointly sufficient for an arbitrary c`adl`ag 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.