@article{AIHPB_2005__41_2_197_0, author = {Bass, Richard F. and Burdzy, Krzysztof and Chen, Zhen-Qing}, title = {Uniqueness for reflecting brownian motion in lip domains}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {197--235}, publisher = {Elsevier}, volume = {41}, number = {2}, year = {2005}, doi = {10.1016/j.anihpb.2004.06.001}, mrnumber = {2124641}, zbl = {1067.60036}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2004.06.001/} }
TY - JOUR AU - Bass, Richard F. AU - Burdzy, Krzysztof AU - Chen, Zhen-Qing TI - Uniqueness for reflecting brownian motion in lip domains JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 197 EP - 235 VL - 41 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2004.06.001/ DO - 10.1016/j.anihpb.2004.06.001 LA - en ID - AIHPB_2005__41_2_197_0 ER -
%0 Journal Article %A Bass, Richard F. %A Burdzy, Krzysztof %A Chen, Zhen-Qing %T Uniqueness for reflecting brownian motion in lip domains %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 197-235 %V 41 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2004.06.001/ %R 10.1016/j.anihpb.2004.06.001 %G en %F AIHPB_2005__41_2_197_0
Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing. Uniqueness for reflecting brownian motion in lip domains. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 2, pp. 197-235. doi : 10.1016/j.anihpb.2004.06.001. http://www.numdam.org/articles/10.1016/j.anihpb.2004.06.001/
[1] On nodal lines of Neumann eigenfunctions, Electron. Comm. Probab. 7 (2002) 129-139, paper 14. | MR | Zbl
, ,[2] On Neumann eigenfunctions in lip domains, J. Amer. Math. Soc. 17 (2004) 243-265. | MR | Zbl
, ,[3] On the “hot spots” conjecture of J. Rauch, J. Funct. Anal. 164 (1999) 1-33. | Zbl
, ,[4] Probabilistic Techniques in Analysis, Springer, New York, 1995. | MR | Zbl
,[5] Uniqueness for the Skorokhod equation with normal reflection in Lipschitz domains, Electron. J. Probab. 1 (11) (1996). | MR | Zbl
,[6] Diffusions and Elliptic Operators, Springer, New York, 1997. | MR | Zbl
,[7] Stochastic differential equations driven by symmetric stable processes, in: Séminaire de Probabilités XXXVI, Springer, New York, 2003, pp. 302-313. | Numdam | MR | Zbl
,[8] Fiber Brownian motion and the ‘hot spots' problem, Duke Math. J. 105 (2000) 25-58. | Zbl
, ,[9] Stochastic differential equations driven by stable processes for which pathwise uniqueness fails, Stochastic Process. Appl. 111 (2004) 1-15. | MR | Zbl
, , ,[10] Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, Ann. Probab. 19 (1991) 486-508. | MR | Zbl
, ,[11] The semimartingale structure of reflecting Brownian motion, Proc. Amer. Math. Soc. 108 (1990) 1007-1010. | MR | Zbl
, ,[12] Pathwise uniqueness for reflecting Brownian motion in Euclidean domains, Probab. Theory Related Fields 117 (2000) 183-200. | MR | Zbl
, ,[13] Censored stable processes, Probab. Theory Related Fields 127 (2003) 89-152. | MR | Zbl
, , ,[14] Brownian paths and cones, Ann. Probab. 13 (1985) 1006-1010. | MR | Zbl
,[15] Coalescence of synchronous couplings, Probab. Theory Related Fields 123 (2002) 553-578. | MR | Zbl
, ,[16] Heat equation and reflected Brownian motion in time dependent domains II, J. Funct. Anal. 204 (2003) 1-34. | MR | Zbl
, , ,[17] Efficient Markovian couplings: examples and counterexamples, Ann. Appl. Probab. 10 (2000) 362-409. | MR | Zbl
, ,[18] Non-polar points for reflected Brownian motion, Ann. Inst. Henri Poincaré Probab. Statist. 29 (1993) 199-228. | Numdam | MR | Zbl
, ,[19] A counterexample to the “hot spots” conjecture, Ann. Math. 149 (1999) 309-317. | Zbl
, ,[20] On reflecting diffusion processes and Skorokhod decomposition, Probab. Theory Related Fields 94 (1993) 281-315. | MR | Zbl
,[21] Pseudo Jordan domains and reflecting Brownian motions, Probab. Theory Related Fields 94 (1992) 271-280. | MR | Zbl
,[22] Reflecting Brownian motions and a deletion result for Sobolev spaces of order , Potential Anal. 5 (1996) 383-401. | MR | Zbl
,[23] Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets, Potential Anal. 2 (1993) 219-243. | MR | Zbl
, , ,[24] SDEs with oblique reflection on nonsmooth domains, Ann. Probab. 21 (1993) 554-580. | MR | Zbl
, ,[25] Convex duality and the Skorokhod Problem I, Probab. Theory Related Fields 115 (1999) 153-195. | MR | Zbl
, ,[26] On the semimartingale representation of reflecting Brownian motion in a cusp, Probab. Theory Related Fields 94 (1993) 505-524. | MR | Zbl
, ,[27] A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash, Arch. Mech. Rat. Anal. 96 (1986) 327-338. | MR | Zbl
, ,[28] Time changes of symmetric Markov processes and a Feynman-Kac formula, J. Theoret. Probab. 2 (1989) 485-501. | MR | Zbl
,[29] Real Analysis, Wiley, 1984. | MR | Zbl
,[30] A construction of reflecting barrier Brownian motions for bounded domains, Osaka J. Math. 4 (1967) 183-215. | MR | Zbl
,[31] Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994. | MR | Zbl
, , ,[32] Construction and decomposition of reflecting diffusions on Lipschitz domains with Hölder cusps, Probab. Theory Related Fields 106 (1996) 521-557. | MR | Zbl
, ,[33] Stochastic Differential Equations and Diffusion Processes, North Holland/Kodansha, Amsterdam, 1989. | MR | Zbl
, ,[34] Boundary Value Problems in Lipschitz Domains, Studies in Partial Differential Equations, Math. Assoc. Amer., Washington, DC, 1982. | MR | Zbl
, ,[35] Mouvement brownien, cônes et processus stables, Probab. Theory Related Fields 76 (1987) 587-627. | MR | Zbl
,[36] Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984) 511-537. | MR | Zbl
, ,[37] Continuous Martingales and Brownian Motion, Springer-Verlag, 1991. | MR | Zbl
, ,[38] Diffusions, Markov Processes, and Martingales, vol. 2, Itô Calculus, Wiley, New York, 1987. | MR | Zbl
, ,[39] Excursions in a cone for two-dimensional Brownian motion, J. Math. Kyoto Univ. 25 (1985) 433-443. | MR | Zbl
,[40] Symmetric Markov Processes, Lect. Notes in Math., vol. 426, Springer, New York, 1974. | MR | Zbl
,[41] Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 24 (1971) 147-225. | MR | Zbl
, ,[42] Multidimensional Diffusion Processes, Springer, New York, 1979. | MR | Zbl
, ,[43] Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probab. Theory Related Fields 96 (1993) 283-317. | MR | Zbl
, ,[44] On reflecting Brownian motion - a weak convergence approach, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 461-488. | Numdam | MR | Zbl
, ,[45] On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1) (1971) 155-167. | MR | Zbl
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