Duke Mathematical Journal

Conditioned Brownian motion in planar domains

Burgess Davis

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Article information

Duke Math. J. Volume 57, Number 2 (1988), 397-421.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]


Davis, Burgess. Conditioned Brownian motion in planar domains. Duke Math. J. 57 (1988), no. 2, 397--421. doi:10.1215/S0012-7094-88-05718-3. http://projecteuclid.org/euclid.dmj/1077307042.

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  • [1] L. Breiman, Probability, Addison-Wesley, Reading, MA, 1968.
  • [2] K. L. Chung, The lifetime of conditional Brownian motion in the plane, Ann. Inst. H. Poincaré Probab. Statist. 20 (1984), no. 4, 349–351.
  • [3] R. Bañuelos, On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains, to appear in Probab. Theory Relat. Fields.
  • [4] M. Cranston and T. R. McConnell, The lifetime of conditioned Brownian motion, Z. Wahrsch. Verw. Gebiete 70 (1985), 1–11.
  • [5] R. D. Deblasse, Doob's conditioned diffusions and their lifetimes, to appear in Ann. Probab.
  • [6] J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 262, Springer-Verlag, New York, 1984.
  • [7] R. Durrett, Brownian Motion and Martingales in Analysis, Wadsworth Mathematics Series, Wadsworth, Belmont, CA, 1984.
  • [8] F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50–74 (1980).
  • [9] W. K. Hayman and Ch. Pommerenke, On analytic functions of bounded mean oscillation, Bull. London Math. Soc. 10 (1978), no. 2, 219–224.
  • [10] M. M. Heins, Topics in Complex Function Theory, Holt, Rinehart, and Winston, New York, 1962.
  • [11] P. W. Jones, Extension theorems for BMO, Indiana Univ. Math. J. 29 (1980), no. 1, 41–66.
  • [12] D. A. Stegenga, A geometric condition which implies BMOA, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, R.I., 1979, pp. 427–430.
  • [13] E. M. Stein, Singular Integrals And Differentiability Properties Of Functions, Princeton Mathematical Series, No. 30, Princeton Univ. Press, Princeton, NJ, 1970.