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Volumn 26, Issue 11-12, 2001, Pages 2037-2080

On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions

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EID: 3242720761     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100107815     Document Type: Article
Times cited : (219)

References (51)
  • 1
    • 33644941420 scopus 로고
    • Positive solutions of elliptic equations in nondivergence form and their adjoints
    • Bauman, P. Positive solutions of elliptic equations in nondivergence form and their adjoints. Ark. Mat. 1984, 22, 153-173.
    • (1984) Ark. Mat. , vol.22 , pp. 153-173
    • Bauman, P.1
  • 2
    • 0034360891 scopus 로고    scopus 로고
    • Bounds for the fundamental solution of elliptic and parabolic equations in nondivergence form
    • Escauriaza, L. Bounds for the fundamental solution of elliptic and parabolic equations in nondivergence form. Comm. Partial Diff. Equations 2000, 25 (5-6), 821-845.
    • (2000) Comm. Partial Diff. Equations , vol.25 , Issue.5-6 , pp. 821-845
    • Escauriaza, L.1
  • 3
    • 0033476786 scopus 로고    scopus 로고
    • On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
    • Albeverio, S.; Bogachev, V.; Röckner, M. On uniqueness of invariant measures for finite- and infinite-dimensional diffusions. Comm. Pure Appl. Math. 1999, 52, 325-362.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 325-362
    • Albeverio, S.1    Bogachev, V.2    Röckner, M.3
  • 4
    • 0034562601 scopus 로고    scopus 로고
    • A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts
    • Bogachev, V.I.; Röckner, M. A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts. Theory Probab. Appl. 2000, 45 (3), 417-436.
    • (2000) Theory Probab. Appl. , vol.45 , Issue.3 , pp. 417-436
    • Bogachev, V.I.1    Röckner, M.2
  • 6
    • 0001184763 scopus 로고
    • An approach to controlled diffusion processes
    • Krylov, N.V. An approach to controlled diffusion processes. Theory Probab. Appl. 1986, 31 (4), 605-626.
    • (1986) Theory Probab. Appl. , vol.31 , Issue.4 , pp. 605-626
    • Krylov, N.V.1
  • 7
    • 84972568429 scopus 로고
    • p-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
    • p-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations. Duke Math. J. 1981, 48, 845-856.
    • (1981) Duke Math. J. , vol.48 , pp. 845-856
    • Fabes, E.B.1    Stroock, D.W.2
  • 8
    • 0039350832 scopus 로고
    • A strong maximum principle for weakly L-subharmonic functions
    • Littman, W. A strong maximum principle for weakly L-subharmonic functions. J. Math. Mech. 1959, 8, 761-770.
    • (1959) J. Math. Mech. , vol.8 , pp. 761-770
    • Littman, W.1
  • 9
    • 0043220226 scopus 로고
    • Generalized subharmonic functions: Monotonic approximations and an improved maximum principle
    • Littman, W. Generalized subharmonic functions: monotonic approximations and an improved maximum principle. Annali Scuola Normale Super. di Pisa Cl. Sci. 1963, 17, 207-222.
    • (1963) Annali Scuola Normale Super. di Pisa Cl. Sci. , vol.17 , pp. 207-222
    • Littman, W.1
  • 10
    • 4243978777 scopus 로고
    • On the adjoint of an elliptic linear differential operator and its potential theory
    • Sjögren, P. On the adjoint of an elliptic linear differential operator and its potential theory. Ark. Mat. 1973, 11, 153-165.
    • (1973) Ark. Mat. , vol.11 , pp. 153-165
    • Sjögren, P.1
  • 20
    • 0003796630 scopus 로고
    • Academic Press: New York
    • Adams, R.A. Sobolev Spaces; Academic Press: New York, 1975; 268 pp.
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 21
    • 21544472496 scopus 로고
    • An inequality in the theory of stochastic integrals
    • Krylov, N.V. An inequality in the theory of stochastic integrals. Theory Probab. Appl. 1971, 16 (3), 438-448.
    • (1971) Theory Probab. Appl. , vol.16 , Issue.3 , pp. 438-448
    • Krylov, N.V.1
  • 22
    • 0001996546 scopus 로고
    • Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation
    • in Russian
    • Krylov, N.V. Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation. Sibirskii Mat. Zhurn. 1976, 17 (2), 290-303 (in Russian);
    • (1976) Sibirskii Mat. Zhurn. , vol.17 , Issue.2 , pp. 290-303
    • Krylov, N.V.1
  • 23
    • 0001996546 scopus 로고
    • English transl.
    • English transl.: Siberian J. Math. 1976, 17 (2), 226-236.
    • (1976) Siberian J. Math. , vol.17 , Issue.2 , pp. 226-236
  • 25
    • 21544452657 scopus 로고
    • j)u = f with continuous coefficients
    • in Russian
    • j)u = f with continuous coefficients. Mat. Sbornik 1982, 118 (3), 399-410 (in Russian);
    • (1982) Mat. Sbornik , vol.118 , Issue.3 , pp. 399-410
    • Semenov, Yu.A.1
  • 26
    • 21544461385 scopus 로고
    • English transl.
    • English transl.: Math. USSR Sbornik 1983, 46 (3), 403-415.
    • (1983) Math. USSR Sbornik , vol.46 , Issue.3 , pp. 403-415
  • 28
    • 53249085341 scopus 로고
    • Regularity of invariant measures on finite and infinite dimensional spaces and applications
    • Bogachev, V.I.; Röckner, M. Regularity of invariant measures on finite and infinite dimensional spaces and applications. J. Funct. Anal. 1995, 133, 168-223.
    • (1995) J. Funct. Anal. , vol.133 , pp. 168-223
    • Bogachev, V.I.1    Röckner, M.2
  • 31
    • 0039437343 scopus 로고
    • Maximum principles for linear, non-uniformly elliptic operators with measurable coefficients
    • Trudinger, N.S. Maximum principles for linear, non-uniformly elliptic operators with measurable coefficients. Math. Z. 1977, 156, 291-301.
    • (1977) Math. Z. , vol.156 , pp. 291-301
    • Trudinger, N.S.1
  • 32
    • 0030600930 scopus 로고    scopus 로고
    • Regularity of invariant measures: The case of non-constant diffusion part
    • Bogachev, V.I.; Krylov, N.V.; Röckner, M. Regularity of invariant measures: the case of non-constant diffusion part. J. Funct. Anal. 1996, 138, 223-242.
    • (1996) J. Funct. Anal. , vol.138 , pp. 223-242
    • Bogachev, V.I.1    Krylov, N.V.2    Röckner, M.3
  • 33
    • 84972513697 scopus 로고
    • Intermediate Schauder theory for second order parabolic equations IV: Time irregularity and regularity
    • Lieberman, G.M. Intermediate Schauder theory for second order parabolic equations IV: time irregularity and regularity. Diff. and Integr. Equations 1992, 5 (6), 1219-1236.
    • (1992) Diff. and Integr. Equations , vol.5 , Issue.6 , pp. 1219-1236
    • Lieberman, G.M.1
  • 35
    • 0019228009 scopus 로고
    • Parabolic interior Schauder estimates by the maximum principle
    • Knerr, B. Parabolic interior Schauder estimates by the maximum principle. Arch. Rational Mech. Anal. 1980, 75, 51-58.
    • (1980) Arch. Rational Mech. Anal. , vol.75 , pp. 51-58
    • Knerr, B.1
  • 36
    • 0001646937 scopus 로고    scopus 로고
    • An Analytic Approach to SPDEs
    • Carmona, R.; Rozovskii, B.; Eds.; Amer. Math. Soc.: Rhode Island, Providence
    • Krylov, N.V. An Analytic Approach to SPDEs. In Stochastic partial differential equations: six perspectives. Carmona, R.; Rozovskii, B.; Eds.; Amer. Math. Soc.: Rhode Island, Providence, 1999; 185-241.
    • (1999) Stochastic Partial Differential Equations: Six Perspectives , pp. 185-241
    • Krylov, N.V.1
  • 38
    • 0004275483 scopus 로고
    • Nauka: Moscow, (in Russian); English transl.: Springer-Verlag: New York
    • Krylov, N.V. Controlled Diffusion Processes. Nauka: Moscow, 1977 (in Russian); English transl.: Springer-Verlag: New York, 1980; 308 pp.
    • (1977) Controlled Diffusion Processes
    • Krylov, N.V.1
  • 40
    • 84972568429 scopus 로고
    • Examples of singular parabolic measures and singular transition probability densities
    • Fabes, E.B.; Kenig, C.E. Examples of singular parabolic measures and singular transition probability densities. Duke Math. J. 1981, 48, 845-856.
    • (1981) Duke Math. J. , vol.48 , pp. 845-856
    • Fabes, E.B.1    Kenig, C.E.2
  • 42
    • 0039764580 scopus 로고
    • Nauka: Moscow, (in Russian); English tranls.: Amer. Math. Soc.: Providence, Rhode Island
    • Portenko, N.I. Generalized Diffusion Processes. Nauka: Moscow, 1982 (in Russian); English tranls.: Amer. Math. Soc.: Providence, Rhode Island, 1990; 180 pp.
    • (1982) Generalized Diffusion Processes
    • Portenko, N.I.1
  • 43
    • 0002021189 scopus 로고
    • Minimization of the Kullback information of diffusion processes
    • Correction: ibid. 1995, 31 (4), 705-707
    • Cattiaux, P.; Léonard, C. Minimization of the Kullback information of diffusion processes. Ann. Inst. H. Poincaré 1994, 30 (1), 83-132; Correction: ibid. 1995, 31 (4), 705-707.
    • (1994) Ann. Inst. H. Poincaré , vol.30 , Issue.1 , pp. 83-132
    • Cattiaux, P.1    Léonard, C.2
  • 44
    • 21544433652 scopus 로고    scopus 로고
    • Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces
    • Univ. Bielefeld, Preprint SFB 343 to appear
    • Krylov, N.V. Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. Univ. Bielefeld, Preprint SFB 343 1999, 99-091; http://www.uni-bielefeld.de/homedir/index.html; to appear in J. Funct. Anal.
    • (1999) J. Funct. Anal. , pp. 99-1091
    • Krylov, N.V.1
  • 45
    • 0003131889 scopus 로고
    • Local behavior of solutions of quasilinear parabolic equations
    • Aronson, D.G.; Serrin, J. Local behavior of solutions of quasilinear parabolic equations. Arch. Rational Mech. Anal. 1967, 25, 81-122.
    • (1967) Arch. Rational Mech. Anal. , vol.25 , pp. 81-122
    • Aronson, D.G.1    Serrin, J.2
  • 46
    • 21544468716 scopus 로고
    • The Harnack inequality for generalized solutions of second order quasilinear parabolic equations
    • in Russian
    • Ivanov, A.V. The Harnack inequality for generalized solutions of second order quasilinear parabolic equations. Trudy Mat. Inst. Steklov 1967, 102, 51-84 (in Russian).
    • (1967) Trudy Mat. Inst. Steklov , vol.102 , pp. 51-84
    • Ivanov, A.V.1
  • 47
    • 84981749879 scopus 로고
    • Pointwise estimates and quasilinear parabolic equations
    • Trudinger, N.S. Pointwise estimates and quasilinear parabolic equations. Comm. Pure Appl. Math. 1968, 21, 205-226.
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 205-226
    • Trudinger, N.S.1
  • 50
    • 0040034302 scopus 로고    scopus 로고
    • Bielefeld Univ., SFB 343 Preprint
    • 1. Bielefeld Univ., SFB 343 Preprint 1999, 99-119, 19 pp.; http:// www.mathematik.uni-bielefeld.de/sfb343.
    • (1999) 1 , pp. 99-119
    • Bogachev, V.I.1    Röckner, M.2    Stannat, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.