Uniqueness for reflecting brownian motion in lip domains
Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 2, pp. 197-235.
@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},
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}
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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, Volume 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] R. Atar, K. Burdzy, On nodal lines of Neumann eigenfunctions, Electron. Comm. Probab. 7 (2002) 129-139, paper 14. | MR | Zbl

[2] R. Atar, K. Burdzy, On Neumann eigenfunctions in lip domains, J. Amer. Math. Soc. 17 (2004) 243-265. | MR | Zbl

[3] R. Bañuelos, K. Burdzy, On the “hot spots” conjecture of J. Rauch, J. Funct. Anal. 164 (1999) 1-33. | Zbl

[4] R.F. Bass, Probabilistic Techniques in Analysis, Springer, New York, 1995. | MR | Zbl

[5] R.F. Bass, Uniqueness for the Skorokhod equation with normal reflection in Lipschitz domains, Electron. J. Probab. 1 (11) (1996). | MR | Zbl

[6] R.F. Bass, Diffusions and Elliptic Operators, Springer, New York, 1997. | MR | Zbl

[7] R.F. Bass, Stochastic differential equations driven by symmetric stable processes, in: Séminaire de Probabilités XXXVI, Springer, New York, 2003, pp. 302-313. | Numdam | MR | Zbl

[8] R.F. Bass, K. Burdzy, Fiber Brownian motion and the ‘hot spots' problem, Duke Math. J. 105 (2000) 25-58. | Zbl

[9] R.F. Bass, K. Burdzy, Z.-Q. Chen, Stochastic differential equations driven by stable processes for which pathwise uniqueness fails, Stochastic Process. Appl. 111 (2004) 1-15. | MR | Zbl

[10] R.F. Bass, E.P. Hsu, Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, Ann. Probab. 19 (1991) 486-508. | MR | Zbl

[11] R.F. Bass, E.P. Hsu, The semimartingale structure of reflecting Brownian motion, Proc. Amer. Math. Soc. 108 (1990) 1007-1010. | MR | Zbl

[12] R.F. Bass, E.P. Hsu, Pathwise uniqueness for reflecting Brownian motion in Euclidean domains, Probab. Theory Related Fields 117 (2000) 183-200. | MR | Zbl

[13] K. Bogdan, K. Burdzy, Z.-Q. Chen, Censored stable processes, Probab. Theory Related Fields 127 (2003) 89-152. | MR | Zbl

[14] K. Burdzy, Brownian paths and cones, Ann. Probab. 13 (1985) 1006-1010. | MR | Zbl

[15] K. Burdzy, Z.-Q. Chen, Coalescence of synchronous couplings, Probab. Theory Related Fields 123 (2002) 553-578. | MR | Zbl

[16] K. Burdzy, Z.-Q. Chen, J. Sylvester, Heat equation and reflected Brownian motion in time dependent domains II, J. Funct. Anal. 204 (2003) 1-34. | MR | Zbl

[17] K. Burdzy, W. Kendall, Efficient Markovian couplings: examples and counterexamples, Ann. Appl. Probab. 10 (2000) 362-409. | MR | Zbl

[18] K. Burdzy, D. Marshall, Non-polar points for reflected Brownian motion, Ann. Inst. Henri Poincaré Probab. Statist. 29 (1993) 199-228. | Numdam | MR | Zbl

[19] K. Burdzy, W. Werner, A counterexample to the “hot spots” conjecture, Ann. Math. 149 (1999) 309-317. | Zbl

[20] Z.-Q. Chen, On reflecting diffusion processes and Skorokhod decomposition, Probab. Theory Related Fields 94 (1993) 281-315. | MR | Zbl

[21] Z.-Q. Chen, Pseudo Jordan domains and reflecting Brownian motions, Probab. Theory Related Fields 94 (1992) 271-280. | MR | Zbl

[22] Z.-Q. Chen, Reflecting Brownian motions and a deletion result for Sobolev spaces of order 1,2, Potential Anal. 5 (1996) 383-401. | MR | Zbl

[23] Z.-Q. Chen, P.J. Fitzsimmons, R.J. Williams, Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets, Potential Anal. 2 (1993) 219-243. | MR | Zbl

[24] P. Dupuis, H. Ishii, SDEs with oblique reflection on nonsmooth domains, Ann. Probab. 21 (1993) 554-580. | MR | Zbl

[25] P. Dupuis, K. Ramanan, Convex duality and the Skorokhod Problem I, Probab. Theory Related Fields 115 (1999) 153-195. | MR | Zbl

[26] R.D. Deblassie, E.H. Toby, On the semimartingale representation of reflecting Brownian motion in a cusp, Probab. Theory Related Fields 94 (1993) 505-524. | MR | Zbl

[27] E.B. Fabes, D.W. Stroock, 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] P.J. Fitzsimmons, Time changes of symmetric Markov processes and a Feynman-Kac formula, J. Theoret. Probab. 2 (1989) 485-501. | MR | Zbl

[29] G.B. Folland, Real Analysis, Wiley, 1984. | MR | Zbl

[30] M. Fukushima, A construction of reflecting barrier Brownian motions for bounded domains, Osaka J. Math. 4 (1967) 183-215. | MR | Zbl

[31] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994. | MR | Zbl

[32] M. Fukushima, M. Tomisaki, Construction and decomposition of reflecting diffusions on Lipschitz domains with Hölder cusps, Probab. Theory Related Fields 106 (1996) 521-557. | MR | Zbl

[33] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland/Kodansha, Amsterdam, 1989. | MR | Zbl

[34] D.S. Jerison, C.E. Kenig, Boundary Value Problems in Lipschitz Domains, Studies in Partial Differential Equations, Math. Assoc. Amer., Washington, DC, 1982. | MR | Zbl

[35] J.-F. Le Gall, Mouvement brownien, cônes et processus stables, Probab. Theory Related Fields 76 (1987) 587-627. | MR | Zbl

[36] P.-L. Lions, A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984) 511-537. | MR | Zbl

[37] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, 1991. | MR | Zbl

[38] L.C.G. Rogers, D. Williams, Diffusions, Markov Processes, and Martingales, vol. 2, Itô Calculus, Wiley, New York, 1987. | MR | Zbl

[39] M. Shimura, Excursions in a cone for two-dimensional Brownian motion, J. Math. Kyoto Univ. 25 (1985) 433-443. | MR | Zbl

[40] M.L. Silverstein, Symmetric Markov Processes, Lect. Notes in Math., vol. 426, Springer, New York, 1974. | MR | Zbl

[41] D.W. Stroock, S.R.S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 24 (1971) 147-225. | MR | Zbl

[42] D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer, New York, 1979. | MR | Zbl

[43] L.M. Taylor, R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probab. Theory Related Fields 96 (1993) 283-317. | MR | Zbl

[44] R.J. Williams, W.A. Zheng, On reflecting Brownian motion - a weak convergence approach, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 461-488. | Numdam | MR | Zbl

[45] T. Yamada, S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1) (1971) 155-167. | MR | Zbl

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