XXIV: 30, 448-452, LNM 1426 (1990)
ÉMERY, Michel;
LÉANDRE, Rémi
Sur une formule de Bismut (
Markov processes,
Stochastic differential geometry)
This note explains why, in Bismut's work on the index theorem, the reference measure is not the Riemannian measure $r$ on the manifold, but $p_1(x,x) r(dx)$, where $p_t(x,y)$ is the density (with respect to $r$!) of the Brownian semi-group
Keywords: Brownian bridge,
Brownian motion in a manifold,
Transformations of Markov processesNature: Exposition,
Original additions
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
XLV: 17, 433-458, LNM 2078 (2013)
ORTMANN, Janosch
Functionals of the Brownian Bridge (
Non commutative probability theory)
Keywords: free Brownian bridge,
semicircular random variablesNature: Original
XLVI: 14, 359-375, LNM 2123 (2014)
ROSENBAUM, Mathieu;
YOR, Marc
On the law of a triplet associated with the pseudo-Brownian bridge (
Theory of Brownian motion)
This article gives a remarkable identity in law which relates the Brownian motion, its local time, and the the inverse of its local time
Keywords: Brownian motion,
pseudo-Brownian bridge,
Bessel process,
local time,
hitting times,
scaling,
uniform sampling,
Mellin transformNature: Original
