Poisson point processes attached to symmetric diffusions
Fukushima, Masatoshi ; Tanaka, Hiroshi
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 419-459 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2005__41_3_419_0,
     author = {Fukushima, Masatoshi and Tanaka, Hiroshi},
     title = {Poisson point processes attached to symmetric diffusions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {419-459},
     doi = {10.1016/j.anihpb.2004.10.004},
     mrnumber = {2139028},
     zbl = {1083.60065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_3_419_0}
}

Fukushima, Masatoshi; Tanaka, Hiroshi. Poisson point processes attached to symmetric diffusions. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 419-459. doi : 10.1016/j.anihpb.2004.10.004. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_3_419_0/

[1] R.M. Blumenthal, Excursions of Markov Processes, Birkhäuser, Boston, 1992. | MR 1138461 | Zbl 0983.60504

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

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

[4] C. Dellacherie, P.A. Meyer, Probabilités et potentiel, Chap. XII, Hermann, Paris, 1987. | MR 488194

[5] C. Dellacherie, B. Maisonneuve, P.A. Meyer, Probabilités et potentiel, Chap. XVII-XXIV, Hermann, Paris, 1992.

[6] E.B. Dynkin, An application of flows to time shift and time reversal in stochastic processes, Trans. Amer. Math. Soc. 287 (1985) 613-619. | MR 768728 | Zbl 0562.60076

[7] P.J. Fitzsimmons, On the excursions of Markov processes in classical duality, Probab. Theory Related Fields 75 (1987) 159-178. | MR 885460 | Zbl 0616.60070

[8] M. Fukushima, On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities, J. Math. Soc. Japan 21 (1969) 58-93. | MR 236998 | Zbl 0181.20903

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

[10] R.K. Getoor, Excursions of a Markov process, Ann. Probab. 7 (1979) 244-266. | MR 525052 | Zbl 0399.60069

[11] R.K. Getoor, Excessive Measures, Birkhäuser, 1990. | MR 1093669 | Zbl 0982.31500

[12] R.K. Getoor, M.J. Sharpe, Excursions of dual processes, Adv. Math. 45 (1982) 259-309. | MR 673804 | Zbl 0497.60067

[13] N. Ikeda, S. Watanabe, The local structure of a class of diffusions and related problems, in: Lecture Notes in Math., vol. 330, 1973, pp. 124-159. | MR 451425 | Zbl 0264.60052

[14] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, 1981. | MR 637061 | MR 1011252 | Zbl 0684.60040

[15] K. Itô, Poisson point processes attached to Markov processes, in: Proc. Sixth Berkeley Symp. Math. Statist. Probab. III, 1970, pp. 225-239. | MR 402949 | Zbl 0284.60051

[16] K. Itô, H.P. Mckean, Diffusion Processes and Their Sample Paths, Springer, 1970. | Zbl 0127.09503

[17] D. Kim, On spectral gaps and exit time distributions for a non-smooth domain, Forum Math., in press. | MR 2254385 | Zbl 1114.31005 | Zbl 05141417

[18] Y. Le Jan, Dual Markovian semigroups and processes, in: Functional Analysis in Markov Processes, Proceedings, Katata and Kyoto, 1981, Lecture Notes in Math., vol. 923, 1982, pp. 47-75. | MR 661618 | Zbl 0484.60060

[19] Z.M. Ma, M. Röckner, Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, 1992. | MR 1214375 | Zbl 0826.31001

[20] P.A. Meyer, Processus de Poisson ponctuels, d'aprés K. Itô, in: Séminaire de Probab. V, Lecture Notes in Math., vol. 191, Springer, Berlin, 1971, pp. 177-190. | Numdam | MR 388551

[21] P.A. Meyer, Note sur l'interprétation des measures d'équilibre, in: Séminaire de Probab. VII, Lecture Notes in Math., vol. 321, 1973, pp. 210-216. | Numdam | MR 373030 | Zbl 0262.60055

[22] M. Nagasawa, Time reversion of Markov processes, Nagoya Math. J. 24 (1964) 177-204. | MR 169290 | Zbl 0133.10702

[23] L.C.G. Rogers, Itô excursion theory via resolvents, Z. Wahrsch. Verw. Gebiete 63 (1983) 237-255. | MR 701528 | Zbl 0528.60073

[24] T.S. Salisbury, On the Itô excursion process, Probab. Theory Related Fields 73 (1986) 319-350. | MR 859837 | Zbl 0587.60067

[25] T.S. Salisbury, Construction of right processes from excursions, Probab. Theory Related Fields 73 (1986) 351-367. | MR 859838 | Zbl 0587.60068