## The Annals of Probability

### Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$

Christer Borell

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 21, Number 1 (1993), 482-489.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989412

Digital Object Identifier
doi:10.1214/aop/1176989412

Mathematical Reviews number (MathSciNet)
MR1207234

Zentralblatt MATH identifier
0776.35024

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J65: Brownian motion [See also 58J65] 58G11

#### Citation

Borell, Christer. Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$. Ann. Probab. 21 (1993), no. 1, 482--489. doi:10.1214/aop/1176989412. https://projecteuclid.org/euclid.aop/1176989412