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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

Retrieve article from Numdam

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

Retrieve article from Numdam

XXXI: 29, 306-314, LNM 1655 (1997)

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

Retrieve article from Numdam