@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}, volume = {38}, year = {2002}, pages = {507-556}, mrnumber = {1914938}, zbl = {0997.60084}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 38 (2002) pp. 507-556. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_4_507_0/
[1] Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030
,[2] Convergence of Dirichlet forms and associated Schrödinger operators, J. Funct. Anal. 68 (1986) 130-148. | MR 852657 | Zbl 0633.47027
, , ,[3] Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967) 890-896. | MR 217444 | Zbl 0153.42002
,[4] Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) 81-122. | MR 244638 | Zbl 0154.12001
, ,[5] The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. 55 (1952) 468-519. | MR 47886 | Zbl 0047.09303
,[6] On the skew product of symmetric diffusion processes, Forum Math. 1 (1989) 103-142. | MR 990139 | Zbl 0656.60083
, ,[7] Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. | MR 1303354 | Zbl 0838.31001
, , ,[8] Short time asymptotics and an approximation for heat kernel of a singular diffusion, in: , , , (Eds.), Itô's Stochastic Calculus and Probability Theory, Springer, 1996, pp. 129-139. | MR 1439521 | Zbl 0866.60066
, , ,[9] Diffusion Processes and their Sample Paths, Springer, 1974. | MR 345224 | Zbl 0285.60063 | Zbl 0127.09503
, ,[10] Convergence of heat kernels on a compact manifold, Kyushu J. Math. 51 (1997) 453-524. | MR 1470166 | Zbl 0914.58031
, , ,[11] General boundary conditions for multi-dimensional diffusion processes, J. Math. Kyoto Univ. 10 (1970) 273-335. | MR 270445 | Zbl 0204.41502
,[12] Weak convergence of symmetric diffusion processes, Probab. Theory Related Fields 109 (1997) 159-187. | MR 1477648 | Zbl 0916.31006
, ,[13] Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr., American Mathematical Society, 1968. | Zbl 0174.15403
, , ,[14] Note on convergence of Dirichlet processes, Bull. London Math. Soc. 25 (1993) 353-356. | MR 1222728 | Zbl 0793.31006
, ,[15] Composite media and asymptotic Dirichlet forms, J. Funct. Anal. 123 (1994) 368-421. | MR 1283033 | Zbl 0808.46042
,[16] Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958) 931-954. | MR 100158 | Zbl 0096.06902
,[17] A probabilistic scheme for collapse of metrics, J. Math. Kyoto Univ. 36 (1996) 73-92. | MR 1381540 | Zbl 1002.58521
, ,[18] Superposition of diffusion processes - Feller property, in: Trends in Probability and Related Analysis, World Scientific, 1999, pp. 113-128. | Zbl 1001.60082
, , ,[19] 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] 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] Equations elliptiques du second ordre à coefficients discontinus, Séminaire sur les equations aux dérivées partielles, Collège de France, 1963. | Numdam
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