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 inequalityNature: Original
Retrieve article from Numdam
XXI: 20, 289-302, LNM 1247 (1987)
PITMAN, James W.
Stationary excursions Retrieve article from Numdam
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 Retrieve article from Numdam
XXIII: 21, 248-257, LNM 1372 (1989)
NEVEU, Jacques;
PITMAN, James W.
The branching process in a Brownian excursion Retrieve article from Numdam
XXIII: 23, 275-293, LNM 1372 (1989)
BARLOW, Martin T.;
PITMAN, James W.;
YOR, Marc
On Walsh's Brownian motions Retrieve article from Numdam
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 Retrieve article from Numdam
XXXI: 27, 272-286, LNM 1655 (1997)
PITMAN, James W.;
YOR, Marc
On the lengths of excursions of some Markov processes Retrieve article from Numdam
XXXI: 28, 287-305, LNM 1655 (1997)
PITMAN, James W.;
YOR, Marc
On the relative lengths of excursions derived from a stable subordinator Retrieve article from Numdam
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 bridgeNature: Original Retrieve article from Numdam
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 MotionNature: Original
XLVII: 12, 219-225, LNM 2137 (2015)
PITMAN, Jim
Martingale Marginals Do Not Always Determine ConvergenceNature: Original
