Lifetime of conditioned Brownian motion in Lipschitz domains

  • M. Cranston
Article

Summary

If D∋-ℝ d , d≧3, is bounded and has Lipschitz boundary then the expected lifetime of any Brownian h-path process in D is finite.

Keywords

Stochastic Process Brownian Motion Probability Theory Mathematical Biology Lipschitz Domain 
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References

  1. 1.
    Chung, K.L.: Lectures from Markov processes to Brownian motion. Berlin-Heidelberg-New York: Springer 1982Google Scholar
  2. 2.
    Chung, K.L.: The lifetime of conditional Brownian motion in the plane. Ann. Inst. Henri Poincaré 20, 349–351 (1984)Google Scholar
  3. 3.
    Cranston, M., McConnell, T.R.: The lifetime of conditioned Brownian motion. Z. Wahrscheinlichkeitstheor. Verw. Geb. 65, 1–11 (1983)Google Scholar
  4. 4.
    Dahlberg, B.E.J.: Estimates of harmonic measure. Arch. Rat. Mech. 65, 275–288 (1977)Google Scholar
  5. 5.
    Doob, J.L.: Conditional Brownian motion and the boundary limits of harmonic functions. Bull. Soc. Math. France 85, 431–458 (1957)Google Scholar
  6. 6.
    Hunt, R.A., Wheeden, R.L.: Positive harmonic functions on Lipschitz domains. Trans. Am. Math. Soc. 132, 307–322 (1968)Google Scholar
  7. 7.
    Jerison, D.S., Kenig, C.E.: Boundary behavior of harmonic functions in non-tangentially accessible domains. Adv. Math. 146, 80–147 (1982)Google Scholar
  8. 8.
    Martin, R.S.: Minimal positive harmonic functions. Trans. Am. Math. Soc. 49, 137–172 (1941)Google Scholar
  9. 9.
    Meyer, P.-A.: Processus de Markov: la frontiére de Martin. Lect. Notes Math. 77. Berlin-Heidelberg-New York: Springer 1968Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • M. Cranston
    • 1
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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