Electronic Communications in Probability

Positivity of Brownian Transition Densities

Martin Barlow, Richard Bass, and Krzysztof Burdzy

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Abstract

Let $B$ be a Borel subset of $R^d$ and let $p(t,x,y)$ be the transition densities of Brownian motion killed on leaving $B$. Fix $x$ and $y$ in $B$. If $p(t,x,y)$ is positive for one $t$, it is positive for every value of $t$. Some related results are given.

Article information

Source
Electron. Commun. Probab., Volume 2 (1997), paper no. 4, 43-51.

Dates
Accepted: 24 September 1997
First available in Project Euclid: 26 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1453832499

Digital Object Identifier
doi:10.1214/ECP.v2-983

Mathematical Reviews number (MathSciNet)
MR1484554

Zentralblatt MATH identifier
0890.60073

Subjects
Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 60J65: Brownian motion [See also 58J65]

Keywords
Transition densities Brownian motion eigenvalue expansion fine topology regular points

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Barlow, Martin; Bass, Richard; Burdzy, Krzysztof. Positivity of Brownian Transition Densities. Electron. Commun. Probab. 2 (1997), paper no. 4, 43--51. doi:10.1214/ECP.v2-983. https://projecteuclid.org/euclid.ecp/1453832499


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References

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