Coalescence of synchronous couplings

Probability Theory and Related Fields

Volumn 123, Issue 4, 2002, Pages 553-578

  Burdzy, Krzysztof ^a   Chen, Zhen Qing ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Coupling; Lipschitz domain; Reflected Brownian motion

Indexed keywords

EID: 0036025132     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400200202     Document Type: Article

References (16)

1. Atar, R., Burdzy, K.: On Neumann eigenfunctions in lip domains (preprint), 2002
2. Bañuelos, R., Burdzy, K.: On the "hot spots" conjecture of J. Rauch. J. Func. Anal., 164, 1-33 (1999)
3. Bass, R.F.: Probabilistic Techniques in Analysis, Springer, New York, 1995
4. Bass, R., Hsu, P.: Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains. Ann. Probab., 19, 486-508 (1991)
5. Bass, R., Hsu, E.P.: Pathwise uniqueness for reflecting Brownian motion in Euclidean domains. Probab. Theory Related Fields, 117, 183-200 (2000)
6. Burdzy, K., Chen, Z.,-Q.: Weak convergence of reflecting Brownian motions. Electronic Communications in Probability 3, paper 4, pp. 29-33, 1998
7. Burdzy, K., Chen, Z.-Q., Jones, P.: Synchronous couplings in smooth domains (forthcoming paper), 2002
8. Burdzy, K., Kendall, W.: Efficient Markovian couplings: examples and counterexamples. Ann. Appl. Probab., 10, 362-409 (2000)
9. Chen, Z.-Q.: On reflecting diffusion processes and Skorokhod decompositions. Probab. Theory Rel. Fields, 94, 281-315 (1993)
10. Cranston, M., Le Jan, Y.: On the noncoalescence of a two point Brownian motion reflecting on a circle. Ann. Inst. H. Poincaré, Prob. Stat., 25, 99-107 (1989)
11. 2. Probability Theory and Related Fields, 87, 241-252 (1990)
12. Dupuis, P., Ishii H.: On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics, 35, 31-62 (1991)
13. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes. Walter de Gruyter, Berlin, 1994
14. Nash, J.: Continuity of solutions of parabolic and elliptic equations. Amer. J. Math., 80, 931-954 (1958)
15. Stroock, D.W.: Diffusion semigroups corresponding to uniformly elliptic divergence form operators. Lect. Notes Math., 1321, 316-347, Springer-Verlag, 1988
16. Takeda, M.: On a martingale method for symmetric diffusion processes and its applications. Osaka J. Math., 26, 605-623 (1989)