Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Simple Search

Query:
Enter a query and click »Search«...
Format:
Display: entries per page entries
Zbl 0782.60051
Burdzy, Krzysztof; Marshall, Donald
Hitting a boundary point with reflected Brownian motion.
(English)
[A] SÃ©minaire de probabilitÃ©s XXVI, Lect. Notes Math. 1526, 81-94 (1992). ISBN 3-540-56021-1/pbk

[For the entire collection see Zbl 0754.00008.]\par Consider a reflected Brownian motion $X$ on the half plane $R\sb +\sp 2=\{x=(x\sb 1,x\sb 2):\ x\sb 2\geq 0\}$ with the variable angle of reflection $\theta: R\sp 1\to (-\pi/2,\pi/2)$, assuming that the angle of reflection is measured in the clockwise direction from the inward pointing normal and is a $C\sp{1+\varepsilon}$-function except, possibly, at 0. It is proved that $X$ hits 0 with positive probability iff $$\int\sb 0\sp 1 {1\over y}\exp\left[\int\sb{-1}\sp 1 {\theta(x)x dx\over \pi(x\sp 2+y\sp 2)}\right]\cos\left[\int\sb{-1}\sp 1 {\theta(x)y dx\over \pi(x\sp 2+y\sp 2)}\right]dy< \infty.$$
[B.Grigelionis (Vilnius)]
MSC 2000:
*60J65 Brownian motion

Keywords: hitting probability; Brownian motion; angle of reflection

Citations: Zbl 0754.00008

Highlights
Master Server