Electronic Communications in Probability

Positivity of Brownian Transition Densities

Martin Barlow, Richard Bass, and Krzysztof Burdzy

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Transition densities Brownian motion eigenvalue expansion fine topology regular points

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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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