An invariance principle for Markov processes and brownian particles with singular interaction
Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 2, pp. 217-248. 
@article{AIHPB_1998__34_2_217_0,
     author = {Osada, Hirofumi},
     title = {An invariance principle for {Markov} processes and brownian particles with singular interaction},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {217--248},
     publisher = {Gauthier-Villars},
     volume = {34},
     number = {2},
     year = {1998},
     mrnumber = {1614595},
     zbl = {0914.60041},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1998__34_2_217_0/}
}
TY  - JOUR
AU  - Osada, Hirofumi
TI  - An invariance principle for Markov processes and brownian particles with singular interaction
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1998
SP  - 217
EP  - 248
VL  - 34
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1998__34_2_217_0/
LA  - en
ID  - AIHPB_1998__34_2_217_0
ER  - 
%0 Journal Article
%A Osada, Hirofumi
%T An invariance principle for Markov processes and brownian particles with singular interaction
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1998
%P 217-248
%V 34
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1998__34_2_217_0/
%G en
%F AIHPB_1998__34_2_217_0
Osada, Hirofumi. An invariance principle for Markov processes and brownian particles with singular interaction. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 2, pp. 217-248. http://www.numdam.org/item/AIHPB_1998__34_2_217_0/

[1] A. De Masi Et Al., An invariance principle for reversible Markov processes. Applications to random motions in random environments, Joul. Stat. Phys., Vol. 55, Nos. 3/4 1989, pp. 787-855. | MR | Zbl

[2] D. Durr and M. Pulvirenti, On the vortex flow in bounded domains, Commun. Math. Phys., Vol. 85, 1982, pp. 265-273. | MR | Zbl

[3] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet forms and symmetric Markov processes Walter de Gruyter, 1994. | MR | Zbl

[4] J. Fritz, Gradient dynamics of infinite point systems, Ann. Prob., Vol. 15, 1987, pp. 478-514. | MR | Zbl

[5] J. Goodman , Convergence of the random vortex method, Commun. Pure Appl. Math., Vol. 40, 1987, pp. 189-220. | MR | Zbl

[6] M.Z. Guo, Limit theorems for interacting particle systems. Thesis, Dept. of Mathematics, New York University, 1984.

[7] J.H. Kim, Stochastic calculus related to non-symmetric Dirichlet forms, Osaka Jour. Math., Vol. 24, 1987, pp. 331-371. | MR | Zbl

[8] C. Kipnis and S.R.S. Varadhan, Central limit theorems for additive functional of reversible Markov process and applications to simple exclusions, Commun. Math. Phys., Vol. 104, 1986, pp. 1-19. | MR | Zbl

[9] R. Lang, Unendlich-dimensionale Wienerprocesse mit Wechselwirkung I, Z. Wahrschverw. Gebiete, Vol. 38, 1977, pp. 55-72. | MR | Zbl

[10] R. Lang, Unendlich-dimensionale Wienerprocesse mit Wechselwirkung II, Z. Wahrschverw. Gebiete, Vol. 39, 1978, pp. 277-299. | MR | Zbl

[11] C. Marchioro and M. Pulvirenti, Hydrodynamic in two dimensions and vortex theory, Commun. Math. Phys., Vol. 84, 1982, pp. 483-503. | MR | Zbl

[12] Z.M. Ma and M. Röckner, Introduction to the theory of (non-symmetric) Dirichlet forms, 1992, Springer. | Zbl

[13] S. Olla, Homogenization of diffusion processes in random fields, Ecole Polytechnique, 1994.

[14] H. Osada, Diffusion processes with generators of generalized divergence form, J. Math. Kyoto Univ., Vol. 27, 1987, pp. 597-619. | MR | Zbl

[15] H. Osada, A stochastic differential equation arising from the vortex problem, Proc. Japan Acad., Vol. 61, Ser. A, 1985. | MR | Zbl

[16] H. Osada, Propagation of chaos for the two dimensional Navier-Stokes equation, in Proc. of Taniguchi Symp. Probabilistic Methods in Mathematical Physics, eds Ito K. and Ikeda N., 1987, pp. 303-334 | MR | Zbl

[17] H. Osada, Homogenization of reflecting barrier Brownian motions, Proc. the Taniguchi Workshop at Sanda and Kyoto, 1990, Pitman Research notes in Math., Vol. 283, 1993, pp. 59-74. | MR | Zbl

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

[19] H. Osada, Tagged particle processes and their non-explosion criteria, in preparation.

[20] H. Osada, Positivity of self-diffusion matrix of interacting Brownian particles with hard core, in preparation.

[21] H. Osada and T. Saitoh, An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains, Probab. Theory Relat. Fields, Vol. 101, 1995, pp. 45-63. | MR | Zbl

[22] Y. Oshima, Lecture on Dirichlet Spaces, Univ. Erlangen-Nurnberg, 1988.

[23] S.I. Resnick, Extreme Values, Regular Variation, and Point Processes, Springer 1987 | MR | Zbl

[24] D. Ruelle, Superstable interactions in classical statistical mechanics, Commun. Math. Phys., Vol. 18, 1970, pp. 127-159. | MR | Zbl

[25] T. Shiga, A remark on infinite-dimensional Wiener processes with interactions, Z. Wahrschverw. Gebiete, Vol. 47, 1979, pp. 299-304 | MR | Zbl

[26] H. Spohn, Large scale dynamics of interacting particles Springer-Verlag, 1991. | Zbl

[27] T. Tanemura, Homogenization of a reflecting barrier Brownian motion in a continuum percolation cluster in Rd, Kodai Math. J., Vol. 17, 1994, pp. 228-245. | MR | Zbl

[28] T. Tanemura, A system of infinitely many mutually reflecting Brownian balls in Rd, Probab. Theory Relat. Fields, Vol. 104, 1996, pp. 399-426. | MR | Zbl

[29] S.R.S. Varadhan, Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion, Ann. Inst. Henri Poincaré, Vol. 31, 1, 1995, pp. 273-285. | Numdam | MR | Zbl