Positivity of Brownian Transition Densities

Martin Barlow (University of British Columbia)
Richard F. Bass (University of Washington)
Krzysztof Burdzy (University of Washington)

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.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 43-51

Publication Date: September 24, 1997

DOI: 10.1214/ECP.v2-983

References

  1. R.F. Bass, Probabilistic Techniques in Analysis, Springer, New York, 1995. Math. Review 96e:60001
  2. R.F. Bass and K. Burdzy, Eigenvalue expansions for Brownian motion with an application to occupation times, Electr. J.~Prob. 1 (1996) paper 3, 1-19. Math. Review 97c:60201
  3. W. Feller, An Introduction to Probability theory and its Applications, vol. 2, 2nd ed. Wiley, New York, 1971. Math. Review 42:5292
  4. Nguyen-Xuan-Loc and T. Watanabe, A characterization of fine domains for a certain class of Markov processes with applications to Brelot harmonic spaces. Z. f. Wahrscheinlichkeitsth. 21 (1972) 167-178. Math. Review 47:1136
  5. S.C. Port and C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, New York, 1978. Math. Review 58:11459
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.