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Weak Convergence of Reflected Brownian Motions
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Krzysztof Burdzy, University of Washington Zhen-Qing Chen, Cornell University |
Abstract
We show that if a sequence of domains $D_k$ increases
to a domain $D$ then the reflected Brownian motions in $D_k$'s
converge to the reflected Brownian motion in $D$, under mild
technical assumptions.
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Full text: PDF
Pages: 29-33
Published on: May 23, 1998
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Bibliography
-
R. Ba~nuelos and K. Burdzy,
On the ``hot spots'' conjecture of J.~Rauch. Preprint.
Math Review article not available.
-
R. Bass and K. Burdzy,
A boundary Harnack principle in twisted Holder domains.
Ann. Math. 134, (1991), 253--276.
Math Review link
-
R. Bass and P. Hsu, Some potential theory for reflecting
Brownian motion in Holder and Lipschitz domains. Ann. Probab.,
19, (1991), 486-508.
Math Review link
-
K. Burdzy and W. Werner, A counterexample to the ``hot spots''
conjecture. Preprint.
-
Z.-Q. Chen, On reflecting diffusion processes and
Skorokhod decompositions. Probab. Theory Rel. Fields,
94, (1993), 281-351.
Math Review link
-
Z.-Q. Chen, P.~J. Fitzsimmons and R.J. Williams,
Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets.
Potential Analysis, 2, (1993), 219-243.
Math Review link
-
M. Fukushima, A construction of reflecting barrier Brownian
motions for bounded domains. Osaka J. Math., 4 (1967),
183-215.
Math Review link
-
M. Fukushima, Y. Oshima and M. Takeda.
Dirichlet forms and symmetric Markov processes.
Walter de Gruyter, Berlin, 1994
Math Review link
-
M. Fukushima and M. Tomisaki,
Construction and decomposition of reflecting diffusions
on Lipschitz domains with Holder cusps.
Probab. Theory Rel. Fields, 106 (1996), 521-557.
Math Review link
-
P.L. Lions and A.S. Sznitman, Stochastic differential
equations with reflecting boundary conditions. Comm. Pure Appl.
Math., 37 (1984), 511-537.
Math Review link
-
T.J. Lyons and W. Zheng, A crossing estimate for the
canonical process on a Dirichlet space and a tightness result.
Asterisque, 157-158 (1988), 249-271.
Math Review link
-
V.G. Maz'ja, Sobolev Spaces. Springer--Verlag, Berlin Heidelberg 1985.
Math Review link
-
D.W. Stroock, Diffusion semigroups corresponding to
uniformly elliptic divergence form operator. Lect. Notes Math. 1321,
316-347, Springer-Verlag (1988).
Math Review link
-
M. Takeda, On a martingale method for symmetric
diffusion processes and its applications.
Osaka J. Math. 26 (1989), 605-623.
Math Review link
-
R.J. Williams and W. Zheng, On reflecting Brownian motion-a
weak convergence approach. Ann. Inst. Henri Poincare,
26 (1990), 461-488.
Math Review link
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Electronic Communications in Probability. ISSN: 1083-589X |
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