Feeling boundary by Brownian motion in a ball

Small ball estimates for Brownian motion and the Brownian sheet

Small ball estimates for Brownian motion and the Brownian sheet are obtained when the balls are given by certain H61der norms. As an application, we establish some lira inf results for Gaussian samples of these processes, as well as Chung's LIL in this setting, but now we introduce some notation. Let I = [0, 1 ], with Co(I) the continuous real-valued function f ( . ) on I such that f ( 0 ) = 0....

On Brownian Motion in a Fluid with a Plane Boundary

Broadband boundary effects on Brownian motion.

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Browni...

Simultaneous boundary hitting for a two point reflecting brownian motion

© Springer-Verlag, Berlin Heidelberg New York, 1989, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...

Hitting a Boundary Point with Reflected Brownian Motion

An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.