Open Access
January, 1993 Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$
Christer Borell
Ann. Probab. 21(1): 482-489 (January, 1993). DOI: 10.1214/aop/1176989412


Consider a convex domain $B$ in $\mathbb{R}^n$ and denote by $p(t, x, y)$ the transition probability density of Brownian motion in $B$ killed at the boundary of $B$. The main result in this paper, in particular, shows that the function $s \ln s^np(s^2, x, y), (s, x, y) \in \mathbb{R}_+ \times B^2$, is concave.


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Christer Borell. "Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$." Ann. Probab. 21 (1) 482 - 489, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0776.35024
MathSciNet: MR1207234
Digital Object Identifier: 10.1214/aop/1176989412

Primary: 60J60
Secondary: 58G11 , 60J65

Keywords: Brunn-Minkowski inequality , Concave , transition probability density of killed Brownian motion

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • January, 1993
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