Convergence of local type Dirichlet forms to a non-local type one
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, p. 507-556
@article{AIHPB_2002__38_4_507_0,
     author = {Ogura, Y. and Tomisaki, M. and Tsuchiya, M.},
     title = {Convergence of local type Dirichlet forms to a non-local type one},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {38},
     number = {4},
     year = {2002},
     pages = {507-556},
     zbl = {0997.60084},
     mrnumber = {1914938},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_4_507_0}
}
Ogura, Y.; Tomisaki, M.; Tsuchiya, M. Convergence of local type Dirichlet forms to a non-local type one. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 4, pp. 507-556. http://www.numdam.org/item/AIHPB_2002__38_4_507_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] S. Albeverio, S. Kusuoka, L. Streit, Convergence of Dirichlet forms and associated Schrödinger operators, J. Funct. Anal. 68 (1986) 130-148. | MR 852657 | Zbl 0633.47027

[3] D.G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967) 890-896. | MR 217444 | Zbl 0153.42002

[4] D.G. Aronson, J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) 81-122. | MR 244638 | Zbl 0154.12001

[5] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. 55 (1952) 468-519. | MR 47886 | Zbl 0047.09303

[6] M. Fukushima, Y. Oshima, On the skew product of symmetric diffusion processes, Forum Math. 1 (1989) 103-142. | MR 990139 | Zbl 0656.60083

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

[8] Y. Hashimoto, S. Manabe, Y. Ogura, Short time asymptotics and an approximation for heat kernel of a singular diffusion, in: Ikeda N., Watanabe S., Fukushima M., Kunita H. (Eds.), Itô's Stochastic Calculus and Probability Theory, Springer, 1996, pp. 129-139. | MR 1439521 | Zbl 0866.60066

[9] K. Itô, H.P. Mckean, Diffusion Processes and their Sample Paths, Springer, 1974. | MR 345224 | Zbl 0285.60063 | Zbl 0127.09503

[10] A. Kasue, H. Kumura, Y. Ogura, Convergence of heat kernels on a compact manifold, Kyushu J. Math. 51 (1997) 453-524. | MR 1470166 | Zbl 0914.58031

[11] H. Kunita, General boundary conditions for multi-dimensional diffusion processes, J. Math. Kyoto Univ. 10 (1970) 273-335. | MR 270445 | Zbl 0204.41502

[12] K. Kuwae, T. Uemura, Weak convergence of symmetric diffusion processes, Probab. Theory Related Fields 109 (1997) 159-187. | MR 1477648 | Zbl 0916.31006

[13] O.A. Ladyženskaya, V.A. Solonnikov, N.N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr., American Mathematical Society, 1968. | Zbl 0174.15403

[14] T.J. Lyons, T.S. Zhang, Note on convergence of Dirichlet processes, Bull. London Math. Soc. 25 (1993) 353-356. | MR 1222728 | Zbl 0793.31006

[15] U. Mosco, Composite media and asymptotic Dirichlet forms, J. Funct. Anal. 123 (1994) 368-421. | MR 1283033 | Zbl 0808.46042

[16] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958) 931-954. | MR 100158 | Zbl 0096.06902

[17] Y. Ogura, S. Taniguchi, A probabilistic scheme for collapse of metrics, J. Math. Kyoto Univ. 36 (1996) 73-92. | MR 1381540 | Zbl 1002.58521

[18] Y. Ogura, M. Tomisaki, M. Tsuchiya, Superposition of diffusion processes - Feller property, in: Trends in Probability and Related Analysis, World Scientific, 1999, pp. 113-128. | Zbl 1001.60082

[19] Y. Ogura, M. Tomisaki, M. Tsuchiya, Existence of a strong solution for an integro-differential equation and superposition of diffusion processes, in: Stochastics in Finite/Infinite Dimensions (In honor of Gopinath Kallianpur), Birkhäuser, 2001, pp. 341-359. | MR 1797095 | Zbl 0985.47037

[20] N.I. Portenko, Diffusion in a medium with a semi-transparent diaphragms, in: Stochastic Processes and Related Topics (Stochastic Monographs Vol. 10), Gordon and Breach, 1996, pp. 117-128. | Zbl 0864.60068

[21] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Séminaire sur les equations aux dérivées partielles, Collège de France, 1963. | Numdam