Approximation of arbitrary Dirichlet processes by Markov chains

 Access to full text

 Full (PDF)

1. [1] S. Albeverio, Y.G. Kondratiev and M. RöcknerErgodicity of L2-semigroups and extremality of Gibbs states. J. Funct. Anal., 144, 1997, pp. 394-423. Zbl0880.60098MR1432591
2. [2] S. Albeverio, Z.M. Ma and M. Röckner, : Regularization of Dirichlet spaces and applications. C.R. Acad. Sci. Paris, 314, Série I, 1992, pp. 859-864. Zbl0756.60070MR1166063
3. [3] S. Albeverio, Z.M. Ma and R. Röckner, Characterization of (non-symmetric) Dirichlet forms associated with Hunt processes. Rand. Oper. and Stoch. Equ.3, 1995, pp. 161-179. Zbl0833.60077MR1341121
4. [4] S. Albeverio, Z.M. Ma and M. Röckner, Potential theory of quasi-regular Dirichlet forms without capacity. In: Z.M. Ma et al. (Eds.), Dirichlet forms and Stochastic Processes, 47-53, Berlin: de Gruyter1995. Zbl0844.31005MR1366422
5. [5] S. Albeverio, Z.M. Ma and M. Röckner, Partitions of unity in Sobolev spaces over infinite dimensional state spaces. J. Funct. Anal., 143, 1997, pp. 247-268. Zbl0873.46020MR1428125
6. [6] S. Albeverio, R. Léandre and M. Röckner, Construction of a rotational invariant diffusion on the free loop space. C. R. Acad. Sci. Paris, 316, Série I, 1993, pp. 287-292. Zbl0776.58041MR1205201
7. [7] S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Prob. Rel. Fields89, 1991, pp. 347-386. Zbl0725.60055MR1113223
8. [8] S. Carrillo-Menendez, Processus de Markov associé à une forme de Dirichlet non symmétrique. Z. Wahrsch. verw. Geb., 33, 1975, pp. 139-154. Zbl0299.60058MR386030
9. [9] Z.Q. Chen, Z.M. Ma and M. Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya Math. J., 136, 1994, pp. 1-15. Zbl0811.31002MR1309378
10. [10] C. Dellacherie and P.A. Meyer, Probabilities and potential B. Amsterdam: North-Holland1982. Zbl0494.60002MR745449
11. [11] B.K. Driver and M. Röckner, Construction of diffusions on path and loop spaces of compact Riemannian manifolds. C.R. Acad. Sci. Paris, 315, Série I, 1992, pp. 859-864. Zbl0771.58047MR1181300
12. [12] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence. John Wiley & Sons, New York1986. Zbl0592.60049
13. [13] K.D. Elworthy and Z.M. Ma, Vector fields on mapping spaces and related Dirichlet forms and diffusions. Preprint (1996). Zbl0893.31009MR1613104
14. [14] M. Fukushima, Dirichlet spaces and strong Markov processes. Trans. Amer. Math. Soc., 162, 1971, pp. 185-224. Zbl0254.60055MR295435
15. [15] M. Fukushima, Dirichlet Forms and Markov Processes. North Holland, Amsterdam1980. Zbl0422.31007MR569058
16. [16] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes. Berlin:Walter de Gruyter1994. Zbl0838.31001MR1303354
17. [17] R. Getoor, Markov processes: ray processes and right processes. Lect. Notes in Math., 440. Berlin: Springer1975. Zbl0299.60051MR405598
18. [18] Y. Lejan, Balayage et formes de Dirichlet. Z. Wahrsch. verw. Geb., 37, 1977, pp. 297-319. Zbl0331.60048MR571671
19. [19] Z.M. Ma and M. Röckner, Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Berlin: Springer1992. Zbl0826.31001
20. [20] Z.M. Ma, M. Röckner and T.S. Zhang, Approximation of Hunt processes by Markov chains. In preparation. Zbl0898.31009
21. [21 ] L. Overbeck, Z.M. Ma and M. Röckner, Markov processes associated with Semi-Dirichlet forms. Osaka J. Math., 32, 1995, pp. 97-119. Zbl0834.60086MR1323103
22. [22] L. Overbeck and M. Röckner, Geometric aspects of finite and infinite dimensional Fleming-Viot processes. Random Oper. and Stoch. Equ., 5, 1997, pp. 35-58. Zbl0880.60087MR1443420
23. [23] L. Overbeck, M. Röckner and B. Schmuland, An analytic approach to Fleming-Viot processes with interactive selection, Ann. Prob.23, 1995, pp. 1-36. Zbl0833.60053MR1330758
24. [24] H. Osada, Dirichlet form approach to infinite-dimensional Wiener processes with singular interactions, Commun. Math. Phys., 176,1996, pp. 117-131. Zbl0837.60073MR1372820
25. [25] M. Röckner, Dirichlet forms on infinite dimensional "manifold like" state spaces: a survey of recent results and some prospects for the future. SFB-343-Preprint (1996). To appear in: Probability towards2000. Zbl0978.31007MR1632608
26. [26] M. Röckner and T.S. Zhang, Uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal., 105, 1992, pp. 187-231. Zbl0779.35028MR1156676
27. [27] M. Röckner and T.S. Zhang, Finite dimensional approximation of diffusion processes on infinite dimensional spaces. Stochastics and Stochastic Reports57, 1996, pp. 37-55. Zbl0885.60066MR1407946
28. [28] M.L. Silverstein, Symmetric Markov Processes. Lect. Notes in Maths., 426, Berlin- Heidelberg-New York, Springer1974. Zbl0296.60038MR386032
29. [29] M.T. Sharpe, General theory of Markov processes. New York: Academic Press, 1988. Zbl0649.60079MR958914
30. [30] M.W. Yoshida, Construction of infinite-dimensional interacting diffusion processes through Dirichlet forms, Probab. Th. Rel. Fields, 106, 1996, pp. 265-297. Zbl0859.60068MR1410690