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On the variances of occupation times of conditioned Brownian motion
Author(s):
Biao
Zhang
Journal:
Trans. Amer. Math. Soc.
348
(1996),
173-185.
MSC (1991):
Primary 60J65, 60J05
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Abstract:
We extend some bounds on the variance of the lifetime of two--dimensional Brownian motion, conditioned to exit a planar domain at a given point, to certain domains in higher dimensions. We also give a short ``analytic'' proof of some existing results.
References:
- 1
- R. Bañuelos and B. Davis, A Geometrical Characterization of Intrinsic Ultracontractivity for Planar Domains with Boundaries Given by Graphs of Functions, Indiana University Mathematical Journal 41 (1992), 885--913, MR 94g:60142.
- 2
- M. Cranston, Conditional Brownian Motion, Whitney Squares and the Conditional Gauge Theorem, Seminar on Stochastic Processes, Birkhäuser 17 (1988), 109--119, MR 90j:60078.
- 3
- B. Davis, Conditioned Brownian Motion in Planar Domains, Duke Math. J. 59 (1988), 397--421, MR 89j:60112.
- 4
- B. Davis, Intrinsic Ultracontractivity for Dirichlet Laplacian, J. Funct. Anal. 100 (1991), 163--180, MR 92k:35065.
- 5
- B. Davis and B. Zhang, Moments of the Lifetime of Conditioned Brownian Motion in Cones, Proceedings of the American Mathematical Society, MR 94i:60097.
- 6
- J.L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer--Verlag, Berlin, 1984, MR 85k:31001.
- 7
- R.A. Hunt and R.L. Wheeden, Positive Harmonic Functions on Lipschitz Domains, Trans. Amer. Math. Soc. 132 (1968), 307--322, MR 43:547.
- 8
- P.W. Jones, Extension Theorems for BMO, Indiana Univ. Math. J. 29 (1980), 41--66, MR 89b:42047.
- 9
- D.S. Jerison and C.E. Kenig, Boundary Value Problems on Lipschitz Domain, M.A.A. Studies in Math., Studies in Partial Differential Equations, Walter Littman 23 (1982), 1--68, MR 85f:35057.
- 10
- E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970, MR 44:7280.
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Additional Information:
Biao
Zhang
Affiliation:
address Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
biao@math.purdue.edu
DOI:
10.1090/S0002-9947-96-01486-9
PII:
S 0002-9947(96)01486-9
Keywords:
Conditioned Brownian motion,
$h$-processes
Received by editor(s):
October 24, 1994
Copyright of article:
Copyright
1996,
American Mathematical Society
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