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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 3126

Keywords: Continuous martingales, Bessel processes, Pitman's theorem

Nature: Original

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XXXI: 26, 266-271, LNM 1655 (1997)

**RAUSCHER, Bernhard**

Some remarks on Pitman's theorem (Stochastic calculus)

For certain transient diffusions $X$, local martingales which are functins of $X_t$ and the future infimum $\inf_{u\ge t}X_u$ are constructed. This extends the preceding article 3125

Comment: See also chap. 12 of Yor,*Some Aspects of Brownian Motion Part~II*, BirkhĂ¤user (1997)

Keywords: Continuous martingales, Bessel processes, Diffusion processes, Pitman's theorem

Nature: Original

Retrieve article from Numdam

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

Comment: Extended to more general diffusions in the next article 3126

Keywords: Continuous martingales, Bessel processes, Pitman's theorem

Nature: Original

Retrieve article from Numdam

XXXI: 26, 266-271, LNM 1655 (1997)

Some remarks on Pitman's theorem (Stochastic calculus)

For certain transient diffusions $X$, local martingales which are functins of $X_t$ and the future infimum $\inf_{u\ge t}X_u$ are constructed. This extends the preceding article 3125

Comment: See also chap. 12 of Yor,

Keywords: Continuous martingales, Bessel processes, Diffusion processes, Pitman's theorem

Nature: Original

Retrieve article from Numdam