Necessary and sufficient conditions for the existence of m-perfect processes associated with Dirichlet forms
Albeverio, Sergio ; Ma, Zhi-Ming
Séminaire de probabilités de Strasbourg, Tome 25 (1991), p. 374-406 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1991-01-01
@article{SPS_1991__25__374_0,
     author = {Albeverio, Sergio and Ma, Zhi-Ming},
     title = {Necessary and sufficient conditions for the existence of $m$-perfect processes associated with Dirichlet forms},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {25},
     year = {1991},
     pages = {374-406},
     mrnumber = {1187795},
     zbl = {0752.60062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1991__25__374_0}
}

Albeverio, Sergio; Ma, Zhi-Ming. Necessary and sufficient conditions for the existence of $m$-perfect processes associated with Dirichlet forms. Séminaire de probabilités de Strasbourg, Tome 25 (1991) pp. 374-406. http://gdmltest.u-ga.fr/item/SPS_1991__25__374_0/

[AH1] Albeverio, S., Høegh-Krohn, R.: Quasi-invariant measures, symmetric diffusion processes and quantum fields. In: Les méthodes mathématiques de la théorie quantique des champs, Colloques Internationaux du C.N.R.S., no. 248, Marseille, 23-27 juin 1975, C.N.R.S., 1976. | MR 424030

[AH2] Albeverio, S., Høegh-Krohn, R.: Dirichlet forms and diffusion processes on rigged Hilbert spaces. Z. Wahrscheinlichkeitstheorie verw. Gebiete 40, 1-57 (1977). | MR 455133 | Zbl 0342.60057

[AH3] Albeverio, S., Høegh-Krohn, R.: Hunt processes and analytic potential theory on rigged Hilbert spaces. Ann. Inst. Henri Poincaré, vol. XIII, no. 3, 269-291 (1977). | Numdam | MR 488323 | Zbl 0382.60082

[ABrR] Albeverio, S., Brasche, J., Röckner, M.: Dirichlet forms and generalized Schrödinger operators, pp. 1-42 in Proc. Sønderborg Conf. "Schrödinger operators", Edts. H. Holden, A. Jensen, Lect. Notes Phys. 345, Springer, Berlin (1989). | MR 1037315 | Zbl 0716.35069

[AFHKL] Albeverio, S., Fenstad, J.E., Høegh-Krohn, R., Lindstrøm, T.: Non standard methods in stochastic analysis and mathematical physics, Academic Press, Orlando (1986) | MR 859372 | Zbl 0605.60005

[AHPRS1] Albeverio, S. Hida, T. Potthoff, J., Röckner, M., Streit, L.: Dirichlet forms in terms of white noise analysis I - Construction and QFT examples, Rev. Math. Phys. 1, 291-312 (1990). | MR 1070092 | Zbl 0708.60099

[AHPRS2] Albeverio, S. Hida, T. Potthoff, J., Röckner, M., Streit, L.: Dirichlet forms in terms of white noise analysis II - Closability and Diffusion Processes, Rev. Math. Phys. 1, 313-323 (1990). | MR 1070093 | Zbl 0708.60100

[AK] Albeverio, S., Kusuoka, S.: Maximality of infinite dimensional Dirichlet forms and Høegh-Krohn's model of quantum fields, to appear in Memorial Volume for Raphael Høegh-Krohn. | Zbl 0798.46055

[AKR] Albeverio, S., Kusuoka, S., Röckner, M.: On partial integration in infinite dimensional space and applications to Dirichlet forms, J. London Math. Soc. (1990) | MR 1078180 | Zbl 0667.31010

[AM1] Albeverio, S., Ma, Z.M.: A note on quasicontinuous kernels representing quasi- linear positive maps, BiBoS - Preprint 1990, to appear in Forum Math. | MR 1115954 | Zbl 0726.60076

[AM2] Albeverio, S., Ma, Z.M.: A general correspondence between Dirichlet forms and right processes, BiBoS-Preprint 415 (1990). | MR 1094436

[AM3] Albeverio, S., Ma, Zhi-Ming : Nowhere Radon smooth measures, perturbations of Dirichlet forms and singular quadratic forms, pp. 3-45 in Proc. Bad Honnef Conf.1988, ed. N. Christopeit, K. Helmes, M. Kohlmann Lect. Notes Control and Inform. Sciences 126, Springer, Berlin (1989). | MR 1236053 | Zbl 0681.60075

[AM4] Albeverio, S., Ma, Z.M.: Additive functionals, nowhere Radon and Kato class smooth measure associated with Dirichlet forms, SFB 237 - Preprint. | MR 1173989

[AM5] Albeverio, S., Ma, Z.M.: Perturbation of Dirichlet forms - lower semiboundedness, closability and form cores, SFB 237 - Preprint, to appear in J. Funct. Anal. (1990). | MR 1121617 | Zbl 0743.60071

[AM6] Albeverio, S., Ma, Z.M.: Local property for Dirichlet forms on general metrizable spaces, in preparation.

[AM7] Albeverio, S., Ma, Z.M.: Diffusion processes associated with singular Dirichlet forms, to appear in Proc. Lisboa Conf., Ed. A.B. Cruzeiro, Birkhäuser, New York (1990). | MR 1168065 | Zbl 0751.60072

[AM8] Albeverio, S., Ma, Z.M.: Characterization of Dirichlet spaces associated with symmetric Hunt processes, in preparation.

[AMR1] Albeverio, S., Ma, Z.M., Röckner, M.: in preparation.

[AMR2] Albeverio, S., Ma, Z.M., Röckner, M.: Dirichlet forms and Markov fields - A report on recent developments, to appear in Proc. Evanston Conf. "Diffusion Processes and Related Problems in Analysis", Ed. M. Pinsky, Birkhäuser, New York (1990). | MR 1110172 | Zbl 0719.60077

[ARö1] Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces- closability and a Cameron-Martin formula, J. Funct. Anal., 88, 395-436 (1990). | MR 1038449 | Zbl 0737.46036

[ARö2] Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process, Prob. Theory and Rel. Fields, 83, 405-434 (1989). | MR 1017404 | Zbl 0661.60094

[ARö3] Albeverio, S., Röckner, M.: New developments in theory and applications of Dirichlet forms (with M. Röckner), to appear in "Stochastic Processes, Physics and Geometry", Proc. 2nd Int. Conf. Ascona - Locarno - Como 1988, Ed. S. Albeverio, G. Casati, U. Cattaneo, D. Merlini, R. Moresi, World Scient., Singapore (1990). | MR 1124202

[ARö4] Albeverio, S., Röckner, M.: Stochastic differential equations in infinite dimension: solutions via Dirichlet forms, SFB 237 - Preprint. | MR 1113223

[ARö5] Albeverio, S., Röckner, M.: Infinite dimensional diffusions connected with positive generalized white noise functionals, Edinburgh Preprint (1990), to appear in Proc. Bielefeld Conference "White Noise Analysis", Ed. T. Hida, H. H. Kuo, J. Potthoff, L. Streit. | MR 1160381 | Zbl 0818.60051

[BG] Blumenthal, R.M., Getoor, R.K. (1968). Markov Processes and Potential Theory, Academic Press, New York. | MR 264757 | Zbl 0169.49204

[BoH1] Bouleau, N., Hirsch, F.: Propriétés d'absolue continuité dans les espaces de Dirichlet et applictions aux équations différentielles stochastiques, Sém. de Probabilités, XX, Lect. Notes Maths., Springer. | Numdam | MR 942020 | Zbl 0642.60044

[BoH2] Bouleau, N., Hirsch, F.: Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener, J. Funct. Anal. 69, 229-259 (1986). | MR 865222 | Zbl 0605.60058

[D1] Dynkin, E.B.: Green's and Dirichlet spaces associated with fine Markov processes. J. Funct. Anal. 47, 381-418 (1982). | MR 665023 | Zbl 0488.60083

[D2] Dynkin, E.B.: Green's and Dirichlet spaces for a symmetric Markov transition function. Lecture Notes of the LMS, 1982. | MR 665023 | Zbl 0501.60081

[DM] Dellacherie, C., Meyer, P.A.: Probabilities and Potential, Ch. I-XIII, Vol. A,B, C, North Holland Math. Studies: Hermann, Paris (1978); North Holland, Amsterdam (1982); Elsevier, Amsterdam (1988) (transl. of Probabilités et Potentiel, Hermann, Paris 1966-1988)

[Fi1] Fitzsimmons, P.J. (1988). Markov processes and nonsymmetric Dirichlet forms without regularity. To appear in J. Funct. Anal. | MR 1012207 | Zbl 0686.60077

[Fi2] Fitzsimmons, P.J.: Time Changes of Symmetric Markov Processes and a Feynman-Kac formula, to appear in J. Theoretical Prob. | MR 1011201 | Zbl 0683.60052

[FG] Fitzsimmons, P.J., Getoor, R.K. (1988). On the potential theory of symmetric Markov processes. Math. Annalen., 281, 495-512. | MR 954155 | Zbl 0627.60067

[Fu1] Fukushima, M.: Regular representations of Dirichlet forms. Trans. Amer. Math. Soc. 155, 455-473 (1971). | MR 281256 | Zbl 0248.31007

[Fu2] Fukushima, M.: Dirichlet spaces and strong Markov processes. Trans. Amer. Math. Soc. 162,185-224 (1971). | MR 295435 | Zbl 0254.60055

[Fu3] Fukushima, M.: Dirichlet forms and Markov processes. Amsterdam-Oxford-New York: North Holland 1980. | MR 569058 | Zbl 0422.31007

[Fu4] Fukushima, M.: Basic properties of Brownian motion and a capacity on the Wiener space. J. Math. Soc. Japan 36, 161-175 (1984). | MR 723601 | Zbl 0522.60081

[Fu5] Fukushima, M.: Potentials for symmetric Markov processes and its applications, pp. 119-133 in Proc. 3d Japan-USSR Symp. Prob. Th., Ed. G. Mamyama, J.V. Prokhorov, Lecture Notes Math. 550, Springer (1976). | MR 494514 | Zbl 0349.60077

[FuO] Fuskushima, M., Oshima, Y.: On skew product of symmetric diffusion processes, Forum Math. 2, 103-142 (1989). | MR 990139 | Zbl 0656.60083

[FaR] Fan Ruzong: On absolute continuity of symmetric diffusion processes on Banach spaces, Beijing Prepr. 1989, to appear in Acta Mat. Appl. Sinica

[G1] Getoor, R.K.: On the construction of kernels, Lect. Notes Maths. 465, 443-463 (1986) | Numdam | MR 436342 | Zbl 0321.60056

[G2] Getoor, R.K.: Markov processes: Ray processes and right processes. Lecture Notes in Math. 440, Berlin-Heidelberg-New York: Springer 1975. | MR 405598 | Zbl 0299.60051

[Ka] Kaneko, H.: On (r, p)-capacities for Markov processes, Osaka J. Math. 23 (1986) 325-336. | MR 856891 | Zbl 0633.60090

[Kn] Knight, F.: Note on regularization of Markov processes, Ill. J. Math. 9, 548 - 552 (1965). | MR 177450 | Zbl 0143.20002

[Ku] Kusuoka, S.: Dirichlet forms and diffusion processes on Banach space. J. Fac. Science Univ. Tokyo, Sec. 1A 29, 79-95 (1982). | MR 657873 | Zbl 0496.60079

[KW] Kunita, H., Watanabe, T.: Some theorems concerning resolvents over locally compact spaces, Proc. Vth Berkeley Symp. Math. Stat. and Prob. Vol. II, Berkeley (1967). | MR 214148 | Zbl 0221.60044

[Le1] Le Jan, Y.: Quasi-continuous functions and Hunt processes, J. Math. Soc. Japan, 35, 37-42 (1983). | Zbl 0528.60070

[Le2] Le Jan, Y.: Dual Markovian semigroups and processes, pp. 47-75 in "Functional Analysis in Markov Processes", Ed. M. Fukushima, Lect. Notes Maths. 923 (1982) | MR 661618 | Zbl 0484.60060

[LR] Lyons, T., Röckner, M.: A note on tightness of Capacities associated with Dirichlet forms, Edinburgh Preprint (1990). | MR 1148680

[Me] Meyer, P.A.: Probability and Potentials, Ginn Blaisdell, Massachussetts (1966) | MR 205288 | Zbl 0138.10401

[P] Parthasarathy, K.R.: Probability measures on metric spaces. New York-London: Academic Press 1967. | MR 226684 | Zbl 0153.19101

[R] Röckner, M.: Generalized Markov fields and Dirichlet forms. Acta Appl. Math. 3, 285-311 (1985). | MR 790552 | Zbl 0588.60044

[Sch] Schmuland, B.: An alternative compactification for classical Dirichlet forms on topological vector spaces, Vancouver Preprint (1989). | MR 1079933

[Scha] Schaefer, H.H.: Topological vector spaces, Mac Millan (1987) | MR 193469

[Sh] Sharpe, M.J.: General Theory of Markov Processes, Academic Press, New York (1988). | MR 958914 | Zbl 0649.60079

[Si] Silverstein, M.L.: Symmetric Markov Processes. Lecture Notes in Math. 426. Berlin-Heidelberg-New York: Springer 1974. | MR 386032 | Zbl 0296.60038

[So1] Song Shiqui: The closability of classical Dirichlet forms on infinite dimensional spaces and the Wiener measure, Acad. Sinica Preprint, Beijing

[So2] Song Shiqui: Admissible vectors and their associated Dirichlet forms, Acad. Sinica Preprint, Beijing (1990)

[So3] Song Shiqui: An infinite dimensional analogue of the Albeverio-Röckner's theorem on Fukushima's conjecture, Acad. Sinica Preprint, Beijing (1989)

[Tak] Takeda, M.: On the uniqueness of Markovian self-adjoint extensions of diffusion operators on infinite dimensional spaces, Osaka J. Math. 22, 733-742 (1985) | MR 815442 | Zbl 0611.60074