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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 3313
Keywords: Continuous martingales, Local martingales, Quadratic variation, Maximal process
Nature: Original
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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 3320
Keywords: Maximal process, Seshadri's identity
Nature: Original
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