Approximation of arbitrary Dirichlet processes by Markov chains
Ma, Zhi-Ming ; Röckner, Michael ; Zhang, Tu-Sheng
Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998), p. 1-22 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1998-01-01
@article{AIHPB_1998__34_1_1_0,
     author = {Ma, Zhi-Ming and R\"ockner, Michael and Zhang, Tu-Sheng},
     title = {Approximation of arbitrary Dirichlet processes by Markov chains},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {34},
     year = {1998},
     pages = {1-22},
     mrnumber = {1617733},
     zbl = {0898.31009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1998__34_1_1_0}
}

Ma, Zhi-Ming; Röckner, Michael; Zhang, Tu-Sheng. Approximation of arbitrary Dirichlet processes by Markov chains. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) pp. 1-22. http://gdmltest.u-ga.fr/item/AIHPB_1998__34_1_1_0/

[1] S. Albeverio, Y.G. Kondratiev and M. Röckner Ergodicity of L2-semigroups and extremality of Gibbs states. J. Funct. Anal., 144, 1997, pp. 394-423. | MR 1432591 | Zbl 0880.60098

[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. | MR 1166063 | Zbl 0756.60070

[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. | MR 1341121 | Zbl 0833.60077

[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 Gruyter 1995. | MR 1366422 | Zbl 0844.31005

[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. | MR 1428125 | Zbl 0873.46020

[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. | MR 1205201 | Zbl 0776.58041

[7] S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Prob. Rel. Fields 89, 1991, pp. 347-386. | MR 1113223 | Zbl 0725.60055

[8] S. Carrillo-Menendez, Processus de Markov associé à une forme de Dirichlet non symmétrique. Z. Wahrsch. verw. Geb., 33, 1975, pp. 139-154. | MR 386030 | Zbl 0299.60058

[9] Z.Q. Chen, Z.M. Ma and M. Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya Math. J., 136, 1994, pp. 1-15. | MR 1309378 | Zbl 0811.31002

[10] C. Dellacherie and P.A. Meyer, Probabilities and potential B. Amsterdam: North-Holland 1982. | MR 745449 | Zbl 0494.60002

[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. | MR 1181300 | Zbl 0771.58047

[12] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence. John Wiley & Sons, New York 1986. | Zbl 0592.60049

[13] K.D. Elworthy and Z.M. Ma, Vector fields on mapping spaces and related Dirichlet forms and diffusions. Preprint (1996). | MR 1613104

[14] M. Fukushima, Dirichlet spaces and strong Markov processes. Trans. Amer. Math. Soc., 162, 1971, pp. 185-224. | MR 295435 | Zbl 0254.60055

[15] M. Fukushima, Dirichlet Forms and Markov Processes. North Holland, Amsterdam 1980. | MR 569058 | Zbl 0422.31007

[16] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes. Berlin:Walter de Gruyter 1994. | MR 1303354 | Zbl 0838.31001

[17] R. Getoor, Markov processes: ray processes and right processes. Lect. Notes in Math., 440. Berlin: Springer 1975. | MR 405598 | Zbl 0299.60051

[18] Y. Lejan, Balayage et formes de Dirichlet. Z. Wahrsch. verw. Geb., 37, 1977, pp. 297-319. | MR 571671 | Zbl 0331.60048

[19] Z.M. Ma and M. Röckner, Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Berlin: Springer 1992. | Zbl 0826.31001

[20] Z.M. Ma, M. Röckner and T.S. Zhang, Approximation of Hunt processes by Markov chains. In preparation.

[21 ] L. Overbeck, Z.M. Ma and M. Röckner, Markov processes associated with Semi-Dirichlet forms. Osaka J. Math., 32, 1995, pp. 97-119. | MR 1323103 | Zbl 0834.60086

[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. | MR 1443420 | Zbl 0880.60087

[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. | MR 1330758 | Zbl 0833.60053

[24] H. Osada, Dirichlet form approach to infinite-dimensional Wiener processes with singular interactions, Commun. Math. Phys., 176,1996, pp. 117-131. | MR 1372820 | Zbl 0837.60073

[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 towards 2000. | MR 1632608 | Zbl 0978.31007

[26] M. Röckner and T.S. Zhang, Uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal., 105, 1992, pp. 187-231. | MR 1156676 | Zbl 0779.35028

[27] M. Röckner and T.S. Zhang, Finite dimensional approximation of diffusion processes on infinite dimensional spaces. Stochastics and Stochastic Reports 57, 1996, pp. 37-55. | MR 1407946 | Zbl 0885.60066

[28] M.L. Silverstein, Symmetric Markov Processes. Lect. Notes in Maths., 426, Berlin- Heidelberg-New York, Springer 1974. | MR 386032 | Zbl 0296.60038

[29] M.T. Sharpe, General theory of Markov processes. New York: Academic Press, 1988. | MR 958914 | Zbl 0649.60079

[30] M.W. Yoshida, Construction of infinite-dimensional interacting diffusion processes through Dirichlet forms, Probab. Th. Rel. Fields, 106, 1996, pp. 265-297. | MR 1410690 | Zbl 0859.60068