Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part

Probability Theory and Related Fields

Volumn 127, Issue 4, 2003, Pages 455-495

  Trutnau, Gerald ^a  

^a UNIVERSITÉ PARIS 13   (France)

Author keywords

Boundary value problems for second order elliptic operators; Diffusion processes; Dirichlet spaces; Local time and additive functionals; Potential and capacities

Indexed keywords

EID: 0346271658     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0296-9     Document Type: Article

References (31)

1. Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces closability and a Cameron-Martin formula. J. Funct. Anal. 88, 395-436 (1990)
2. Bass, R.F., Hsu, P.: The semimartingale structure of reflecting Brownian motion. Proc. Amer. Math. Soc. 108 (4), 1007-1010 (1990)
3. Bass, R.F., Hsu, P.: Some potential theory for reflecting Brownian motion in Holder and Lipschitz domains. Ann. Probab. 19 (2), 486-508 (1991)
4. Bouleau, N., Hirsch, F.: Dirichlet forms and Analysis on Wiener space. Walter de Gruyter, Berlin, 1991
5. Chen, Z.-Q.: On reflected Dirichlet spaces. Probab. Theory Relat. Fields 94, 135-162 (1992)
6. Chen, Z.-Q.: On reflecting diffusion processes and Skorokhod decompositions. Probab. Theory Relat. Fields 94, 281-315 (1993)
7. Eberle, A.: Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators. LNM 1718, Springer, 1999
8. Evans, L.C., Gariepy, R.F.: Measure theory and fine properties of functions. Boca Raton: CRC Press, 1992
9. Fradon, M.: Diffusions réfléchies réversibles dégénérées. Potential Analysis 6, 369-414 (1997)
10. Fukushima, M.: A construction of reflecting barrier Brownian motions for bounded domains. Osaka J. Math. 4, 183-215 (1967)
11. Fukushima, M.: Regular representations of Dirichlet spaces. Trans. Amer. Math. Soc. 155, 455-473 (1971)
12. Fukushima, M.,Oshima, Y., Takeda, M.: Dirichlet forms and Symmetric Markov processes. Berlin-New York: Walter de Gruyter, 1994
13. Fukushima, M., Tomisaki, M.: Construction and decomposition of reflecting diffusions on Lipschitz domains with Holder cusps. Probab. Theory Related Fields 106 (4), 521-557 (1996)
14. Kuwae, K.: Reflected Dirichlet forms and the uniqueness of Silverstein's extension. Potential Anal. 16 (3), 221-247 (2002)
15. Kuwae, K., Uemura, T: Weak convergence of symmetric diffusion processes. Prob. Theory Relat. Fields 109 (2), 159-182 (1997)
16. Ma, Z.M., Röckner, M.: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Berlin: Springer, 1992
17. Maz'ja, V.G.: Sobolev spaces. Berlin-Heidelberg, Springer, 1985
18. Oshima, Y: Lectures on Dirichlet spaces. Universität Erlangen-Nürnberg, 1988
19. Pardoux, E., Williams, R.J.: Symmetric reflected diffusions. Ann. Inst. Henri Poincaré 30(1), 13-62 (1994)
20. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Springer, Berlin, 1985
21. Revuz, D.: Mesures associées aux fonctionelles additives de Markov I. Trans. Amer. Math. Soc. 148, 501-531 (1997)
22. Reed, M., Simon, B.: Methods of modern mathematical physics II. Fourier Analysis. Academic Press, New York-San Francisco-London, 1975
23. Silverstein, M.L.: Symmetric Markov Processes. LMN 426, (1974)
24. Silverstein, M.L.: The reflected Dirichlet space. Illinois J. Math. 18, 310-355 (1974)
25. Stannat, W.: The theory of generalized Dirichlet forms and its applications in analysis and stochastics. Mem. Amer. Math. Soc. 142 (678), (1999)
26. 1: Existence, uniqueness and associated Markov processes. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1), 99-140 (1999)
27. 1. Preprint 00-080, Preprintreihe SFB 343 Universität Bielefeld, 2000, extended version 29.1.2002
28. Trutnau, G.: Stochastic calculus of generalized Dirichlet forms and applications to stochastic differential equations in infinite dimensions. Osaka J. Math. 37, 315-343 (2000)
29. Trutnau, G.: On a class of non-symmetric diffusions containing fully non-symmetric distorted Brownian motions. Forum Math. 15 (3), 409-437 (2003)
30. Widder, D.V.: The Laplace transform. Princeton: Princeton University press, 1946
31. Williams, R.J., Zheng, W.A.: On reflecting Brownian motion - a weak convergence approach. Ann. Inst. Henri Poincaré 26 (3), 461-488 (1990)