The Chance of a Long Lifetime for Brownian Motion in a Horn-Shaped Domain

Dante DeBlassie (Texas A&M University)

Abstract


By means of a simple conditioning/comparison argument, we derive the chance of a long lifetime for Brownian motion in a horn-shaped domain.

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

Pages: 134-139

Publication Date: April 24, 2007

DOI: 10.1214/ECP.v12-1263

References

  1. R. Bañuelos, R.D. DeBlassie, and R. Smits (2001). The first exit time of planar Brownian motion from the interior of a parabola. Annals of Probability 29 (2001), 882-901. MR1849181
  2. P. Collet, S. Martinez and J. San Martin. Ratio limit theorems for a Brownian motion killed at the boundary of a Benedicks domain. Annals of Probability 27 (1999), 1160-1182. MR1733144
  3. P. Collet, S. Martinez and J. San Martin. Asymptotic behaviour of a Brownian motion on exterior domains. Probability Theory and Related Fields 116 (2000), 303-316. MR1749277
  4. P. Collet, S. Martinez and J. San Martin. Asymptotic of the heat kernel in general Benedicks domain. Probability Theory and Related Fields 125 (2003), 350-364. MR1964457
  5. P. Collet, S. Martinez and J. San Martin. Ratio limit theorem for parabolic horn-shaped domains. Transactions of the American Mathematical Society 358 (2006), 5059-5082. MR22311885
  6. W. Feller. An Introduction to Probability Theory and its Applications, Volume 2, Second Edition. (1971) Wiley, New York. MR0270403
  7. N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes}, Second Edition. (1989) North-Holland, Amsterdam. MR1011252
  8. W. Li. The first exit time of Brownian motion from an unbounded convex domain. Annals of Probability 31 (2003), 1078-1096. MR1964959
  9. M. Lifshits and Z. Shi. The first exit time of Brownian motion from a parabolic domain. Bernoulli 8 (2002), 745-765. MR1963660
  10. R.G. Pinsky. Positive Harmonic Functions and Diffusion. (1995) Cambridge University Press, Cambridge. MR1326606
  11. M. van den Berg. Subexponential behaviour of the Dirichlet heat kernel. Journal of Functional Analysis 198 (2003), 28-42. MR1962352
Bookmark and Share


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