XXXI: 12, 113-125, LNM 1655 (1997)
ELWORTHY, Kenneth David;
LI, Xu-Mei;
YOR, Marc
On the tails of the supremum and the quadratic variation of strictly local martingales (
Martingale theory)
The asymptotic tails of the current maximum and the quadratic variation of a positive continuous local martingale are compared. Applications to strict local martingales associated with transient diffusions, such as Bessel processes, and remarkable identities for Bessel functions are given
Comment: In discrete time, see the following article
3113. Related results are due to Takaoka
3313Keywords: Continuous martingales,
Local martingales,
Quadratic variation,
Maximal processNature: Original
Retrieve article from Numdam
XXXI: 29, 306-314, LNM 1655 (1997)
YOR, Marc
Some remarks about the joint law of Brownian motion and its supremum (
Brownian motion)
Seshadri's identity says that if $S_1$ denotes the maximum of a Brownian motion $B$ on the interval $[0,1]$, the r.v. $2S_1(S_1-B_1)$ is independent of $B_1$ and exponentially distributed. Several variants of this are obtained
Comment: See also
3320Keywords: Maximal process,
Seshadri's identityNature: Original Retrieve article from Numdam
