XXXI: 25, 256-265, LNM 1655 (1997)
TAKAOKA, Koichiro
On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem (
Stochastic calculus)
Martingales involving the future minimum of a transient Bessel process are studied, and shown to satisfy a non Markovian SDE. In dimension $>3$, uniqueness in law does not hold for this SDE. This generalizes Saisho-Tanemura
Tokyo J. Math. 13 (1990)
Comment: Extended to more general diffusions in the next article
3126Keywords: Continuous martingales,
Bessel processes,
Pitman's theoremNature: Original
Retrieve article from Numdam
XXXIII: 13, 327-333, LNM 1709 (1999)
TAKAOKA, Koichiro
Some remarks on the uniform integrability of continuous martingales (
Martingale theory)
For a continuous local martingale which converges a.s., a general relation links the asymptotic tails of the maximal variable and the quadratic variation. This unifies previous results by Azéma-Gundy-Yor
1406, Elworthy-Li-Yor
3112 and
Probab. Theory Related Fields 115 (1999)
Keywords: Uniform integrability,
Continuous martingales,
Local martingalesNature: Original Retrieve article from Numdam
