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] Séminaire de probabilités 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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]