메뉴 건너뛰기




Volumn 113, Issue 1, 2004, Pages 37-64

On weak uniqueness for some diffusions with discontinuous coefficients

Author keywords

Second order elliptic equations; Stochastic It equations; Weak uniqueness

Indexed keywords


EID: 4243125229     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.03.012     Document Type: Article
Times cited : (47)

References (26)
  • 1
    • 0001224167 scopus 로고
    • Uniqueness for diffusions with piecewise constant coefficients
    • Bass R. Pardoux E. Uniqueness for diffusions with piecewise constant coefficients Probab. Theory Related Fields 76 1987 557-572
    • (1987) Probab. Theory Related Fields , vol.76 , pp. 557-572
    • Bass, R.1    Pardoux, E.2
  • 2
    • 84871414400 scopus 로고
    • 1,2 solvability for the Cauchy - Dirichlet problem for parabolic equations with VMO coefficients
    • 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients Comm. Partial Differential Equations 18 9-10 1993 1735-1763
    • (1993) Comm. Partial Differential Equations , vol.18 , Issue.9-10 , pp. 1735-1763
    • Bramanti, M.1    Cerutti, M.C.2
  • 3
    • 0000944797 scopus 로고
    • Uniqueness in the Dirichlet problem for some elliptic operators with discontinuous coefficients
    • Cerutti M.C. Escauriaza L. Fabes E.B. Uniqueness in the Dirichlet problem for some elliptic operators with discontinuous coefficients Ann. Mat. Pura Appl. 163 4 1993 161-180
    • (1993) Ann. Mat. Pura Appl. , vol.163 , Issue.4 , pp. 161-180
    • Cerutti, M.C.1    Escauriaza, L.2    Fabes, E.B.3
  • 4
    • 0009361007 scopus 로고    scopus 로고
    • Uniqueness for elliptic equations with time-independent coefficients. Progress in Elliptic and Parabolic Partial Differential Equations, Capri, 1994
    • Longman, Harlow
    • Cerutti M.C. Fabes E.B. Manselli P. 1996. Uniqueness for elliptic equations with time-independent coefficients. Progress in Elliptic and Parabolic Partial Differential Equations, Capri, 1994, Pitman Res. Notes Math. Ser., 350, Longman, Harlow, pp. 112-135
    • (1996) Pitman Res. Notes Math. Ser. , vol.350 , pp. 112-135
    • Cerutti, M.C.1    Fabes, E.B.2    Manselli, P.3
  • 5
    • 0011050750 scopus 로고
    • The factorization of nonnegative definite matrices
    • (in Russian)
    • Freidlin M.I. The factorization of nonnegative definite matrices Teor. Verojatnost. i Primenen. 13 2 1968 375-378 (in Russian)
    • (1968) Teor. Verojatnost. I Primenen. , vol.13 , Issue.2 , pp. 375-378
    • Freidlin, M.I.1
  • 6
    • 4243175083 scopus 로고
    • The martingale problem for a differential operator with piecewise continuous coefficients. Seminar on Stochastic Processes, Seattle, WA, 1992
    • Birkhäuser, Boston, MA
    • Gao P. 1993. The martingale problem for a differential operator with piecewise continuous coefficients. Seminar on Stochastic Processes, Seattle, WA, 1992, Progress in Probability, Vol. 33, Birkhäuser, Boston, MA, pp. 135-141
    • (1993) Progress in Probability , vol.33 , pp. 135-141
    • Gao, P.1
  • 7
    • 0003259059 scopus 로고
    • Elliptic partial differential equations of second order
    • 2nd Edition. Springer, Berlin
    • Gilbarg D. Trudinger N.S. 1983. Elliptic partial differential equations of second order, 2nd Edition. Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer, Berlin
    • (1983) Grundlehren Der Mathematischen Wissenschaften , vol.224
    • Gilbarg, D.1    Trudinger, N.S.2
  • 9
    • 0010922516 scopus 로고    scopus 로고
    • On averaging principle for diffusion processes with null-recurrent fast component
    • Khasminskii R. Krylov N.V. On averaging principle for diffusion processes with null-recurrent fast component Stochastic Process Appl. 93 2 2001 229-240
    • (2001) Stochastic Process Appl. , vol.93 , Issue.2 , pp. 229-240
    • Khasminskii, R.1    Krylov, N.V.2
  • 10
    • 34250495424 scopus 로고
    • Diffusion in the plane with reflection. Construction of the process
    • (in Russian) (English translation in Siberian Math. J. 10 (2), 244-252)
    • Krylov N.V. Diffusion in the plane with reflection. Construction of the process Sibirski Mat. J. 10 2 1969 343-354 (in Russian) (English translation in Siberian Math. J. 10 (2), 244-252)
    • (1969) Sibirski Mat. J. , vol.10 , Issue.2 , pp. 343-354
    • Krylov, N.V.1
  • 11
    • 4243192896 scopus 로고
    • On the regularity of the conditional probability for stochastic processes
    • (in Russian) (English translation: Theor. Probab. Appl. 18(1), 150-153)
    • Krylov N.V. On the regularity of the conditional probability for stochastic processes Teoriya Veroyatnostei i eye Primeneniya 18 1 1973 151-155 (in Russian) (English translation: Theor. Probab. Appl. 18(1), 150-153)
    • (1973) Teoriya Veroyatnostei I Eye Primeneniya , vol.18 , Issue.1 , pp. 151-155
    • Krylov, N.V.1
  • 12
    • 0000538250 scopus 로고
    • On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes
    • (in Russian) (English translation in Math. USSR Izvestija 7(3), 691-709)
    • Krylov N.V. On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes Izv. Akad. Nauk SSSR Ser. Mat. 37 3 1973 691-708 (in Russian) (English translation in Math. USSR Izvestija 7(3), 691-709)
    • (1973) Izv. Akad. Nauk SSSR Ser. Mat. , vol.37 , Issue.3 , pp. 691-708
    • Krylov, N.V.1
  • 13
    • 0004275483 scopus 로고
    • Moscow: Nauka, (in Russian) (English translation: Springer, Berlin, 1980)
    • Krylov N.V. Controlled Diffusion Processes 1977 Nauka Moscow (in Russian) (English translation: Springer, Berlin, 1980)
    • (1977) Controlled Diffusion Processes
    • Krylov, N.V.1
  • 14
    • 0013260916 scopus 로고
    • Once more about the connection between elliptic operators and Itô's stochastic equations
    • Optimiz. Software Inc., Publications Division, New York
    • Krylov N.V. 1985. Once more about the connection between elliptic operators and Itô's stochastic equations. In: Statistics and Control of Stoch. Proceedings of the Steklov Seminar 1984; Optimiz. Software Inc., Publications Division, New York, 1985, pp. 214-229
    • (1985) Statistics and Control of Stoch. Proceedings of the Steklov Seminar 1984 , pp. 214-229
    • Krylov, N.V.1
  • 15
    • 0013262021 scopus 로고
    • An approach in the theory of controlled diffusion processes
    • (in Russian) (English translation: Theor. Probab. Appl. 31(4), (1987) 604-626)
    • Krylov N.V. An approach in the theory of controlled diffusion processes Teoriya Veroyatnostei i eye Primeneniya 31 4 1986 685-709 (in Russian) (English translation: Theor. Probab. Appl. 31(4), (1987) 604-626)
    • (1986) Teoriya Veroyatnostei I Eye Primeneniya , vol.31 , Issue.4 , pp. 685-709
    • Krylov, N.V.1
  • 16
    • 84954686497 scopus 로고
    • On one-point weak uniqueness for elliptic equations
    • Krylov N.V. On one-point weak uniqueness for elliptic equations Comm. PDE 17 1992 1759-1784
    • (1992) Comm. PDE , vol.17 , pp. 1759-1784
    • Krylov, N.V.1
  • 19
    • 4243179604 scopus 로고
    • On elliptic equations with piecewise constant coefficients II
    • Lorenzi A. On elliptic equations with piecewise constant coefficients II Ann. Scuola Norm. Sup. Pisa 26 3 1972 839-870
    • (1972) Ann. Scuola Norm. Sup. Pisa , vol.26 , Issue.3 , pp. 839-870
    • Lorenzi, A.1
  • 20
    • 84972574822 scopus 로고
    • On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations
    • Nakao S. On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations Osaka J. Math. 9 1972 513-518
    • (1972) Osaka J. Math. , vol.9 , pp. 513-518
    • Nakao, S.1
  • 21
    • 85129288462 scopus 로고    scopus 로고
    • Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
    • Nadirashvili N.S. Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 4 1997 537-550
    • (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.24 , Issue.4 , pp. 537-550
    • Nadirashvili, N.S.1
  • 22
    • 0013481838 scopus 로고
    • Elliptic-parabolic equations of the second order
    • Phillips R.S. Sarason L. Elliptic-parabolic equations of the second order J. Math. Mech. 17 2 1968 891-917
    • (1968) J. Math. Mech. , vol.17 , Issue.2 , pp. 891-917
    • Phillips, R.S.1    Sarason, L.2
  • 24
    • 0000738072 scopus 로고
    • On a weak uniqueness for some elliptic equations
    • Safonov M.V. On a weak uniqueness for some elliptic equations Comm. Partial Differential Equations 19 5-6 1994 943-957
    • (1994) Comm. Partial Differential Equations , vol.19 , Issue.5-6 , pp. 943-957
    • Safonov, M.V.1
  • 25
    • 0033243615 scopus 로고    scopus 로고
    • Nonuniqueness for second-order elliptic equations with measurable coefficients
    • Safonov M.V. Nonuniqueness for second-order elliptic equations with measurable coefficients SIAM J. Math. Anal. 30 4 1999 879-895
    • (1999) SIAM J. Math. Anal. , vol.30 , Issue.4 , pp. 879-895
    • Safonov, M.V.1
  • 26
    • 0003439179 scopus 로고
    • Multidimensional diffusion processes
    • New York: Springer
    • Stroock D.W. Varadhan S.R.S. Multidimensional diffusion processes 1979 Springer New York
    • (1979)
    • Stroock, D.W.1    Varadhan, S.R.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.