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XV: 17, 251-258, LNM 850 (1981)

**PITMAN, James W.**

A note on $L_2$ maximal inequalities (Martingale theory)

This paper contains a $L^2$ inequality between two processes $(X_n,M_n)$ under assumptions which (if $X$ is a martingale) apply to $M_n=\sup_{m\le n} |X_m|$, and to other interesting cases as well. In particular, Doob's inequality is valid for the larger process $\sup_{m\le n} X_m^+ +\sup_{m\le n} X_m^-$

Keywords: Maximal inequality, Doob's inequality

Nature: Original

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XXI: 20, 289-302, LNM 1247 (1987)

**PITMAN, James W.**

Stationary excursions

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XXIII: 20, 239-247, LNM 1372 (1989)

**NEVEU, Jacques**; **PITMAN, James W.**

Renewal property of the extrema and tree property of the excursion of a one-dimensional Brownian motion

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XXIII: 21, 248-257, LNM 1372 (1989)

**NEVEU, Jacques**; **PITMAN, James W.**

The branching process in a Brownian excursion

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XXIII: 23, 275-293, LNM 1372 (1989)

**BARLOW, Martin T.**; **PITMAN, James W.**; **YOR, Marc**

On Walsh's Brownian motions

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XXIII: 24, 294-314, LNM 1372 (1989)

**BARLOW, Martin T.**; **PITMAN, James W.**; **YOR, Marc**

Une extension multidimensionnelle de la loi de l'arc sinus

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XXXI: 27, 272-286, LNM 1655 (1997)

**PITMAN, James W.**; **YOR, Marc**

On the lengths of excursions of some Markov processes

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XXXI: 28, 287-305, LNM 1655 (1997)

**PITMAN, James W.**; **YOR, Marc**

On the relative lengths of excursions derived from a stable subordinator

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XXXIII: 20, 388-394, LNM 1709 (1999)

**PITMAN, James W.**

The distribution of local times of a Brownian bridge (Brownian motion)

Several useful identities for the one-dimensional marginals of local times of Brownian bridges are derived. This is a variation and extension on the well-known joint law of the maximum and the value of Brownian motion at a given time

Comment: Useful references are Borodin,*Russian Math. Surveys* (1989) and the book *Brownian motion and stochastic calculus* by Karatzas-Shrieve (Springer, 1991)

Keywords: Local times, Brownian bridge

Nature: Original

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XXXIX: 14, 269-303, LNM 1874 (2006)

**ALDOUS, David**; **PITMAN, James W.**

Two recursive decompositions of Brownian bridge related to the asymptotics of random mappings

XLVII: 06, 49-88, LNM 2137 (2015)

**PITMAN, Jim**; **TANG, Wenpin**

Patterns in Random Walks and Brownian Motion

Nature: Original

XLVII: 12, 219-225, LNM 2137 (2015)

**PITMAN, Jim**

Martingale Marginals Do Not Always Determine Convergence

Nature: Original

A note on $L_2$ maximal inequalities (Martingale theory)

This paper contains a $L^2$ inequality between two processes $(X_n,M_n)$ under assumptions which (if $X$ is a martingale) apply to $M_n=\sup_{m\le n} |X_m|$, and to other interesting cases as well. In particular, Doob's inequality is valid for the larger process $\sup_{m\le n} X_m^+ +\sup_{m\le n} X_m^-$

Keywords: Maximal inequality, Doob's inequality

Nature: Original

Retrieve article from Numdam

XXI: 20, 289-302, LNM 1247 (1987)

Stationary excursions

Retrieve article from Numdam

XXIII: 20, 239-247, LNM 1372 (1989)

Renewal property of the extrema and tree property of the excursion of a one-dimensional Brownian motion

Retrieve article from Numdam

XXIII: 21, 248-257, LNM 1372 (1989)

The branching process in a Brownian excursion

Retrieve article from Numdam

XXIII: 23, 275-293, LNM 1372 (1989)

On Walsh's Brownian motions

Retrieve article from Numdam

XXIII: 24, 294-314, LNM 1372 (1989)

Une extension multidimensionnelle de la loi de l'arc sinus

Retrieve article from Numdam

XXXI: 27, 272-286, LNM 1655 (1997)

On the lengths of excursions of some Markov processes

Retrieve article from Numdam

XXXI: 28, 287-305, LNM 1655 (1997)

On the relative lengths of excursions derived from a stable subordinator

Retrieve article from Numdam

XXXIII: 20, 388-394, LNM 1709 (1999)

The distribution of local times of a Brownian bridge (Brownian motion)

Several useful identities for the one-dimensional marginals of local times of Brownian bridges are derived. This is a variation and extension on the well-known joint law of the maximum and the value of Brownian motion at a given time

Comment: Useful references are Borodin,

Keywords: Local times, Brownian bridge

Nature: Original

Retrieve article from Numdam

XXXIX: 14, 269-303, LNM 1874 (2006)

Two recursive decompositions of Brownian bridge related to the asymptotics of random mappings

XLVII: 06, 49-88, LNM 2137 (2015)

Patterns in Random Walks and Brownian Motion

Nature: Original

XLVII: 12, 219-225, LNM 2137 (2015)

Martingale Marginals Do Not Always Determine Convergence

Nature: Original