메뉴 건너뛰기




Volumn 254, Issue 1, 2008, Pages 109-153

Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients

Author keywords

Absolutely continuous solutions; Existence and uniqueness almost everywhere; Fokker Planck equation; Martingale solutions

Indexed keywords


EID: 36649027622     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.09.020     Document Type: Article
Times cited : (223)

References (18)
  • 1
    • 7544243351 scopus 로고    scopus 로고
    • Transport equation and Cauchy problem for BV vector fields
    • Ambrosio L. Transport equation and Cauchy problem for BV vector fields. Invent. Math. 158 2 (2004) 227-260
    • (2004) Invent. Math. , vol.158 , Issue.2 , pp. 227-260
    • Ambrosio, L.1
  • 2
    • 36649020773 scopus 로고    scopus 로고
    • L. Ambrosio, Lecture notes on transport equation and Cauchy problem for non-smooth vector fields, preprint, 2005, available at http://cvgmt.sns.it
  • 3
    • 36649034132 scopus 로고    scopus 로고
    • L. Ambrosio, G. Crippa, Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields, preprint, 2006
  • 4
    • 31744443874 scopus 로고    scopus 로고
    • Gradient Flows in Metric Spaces and in the Wasserstein Space of Probability Measures
    • Birkhäuser, Basel
    • Ambrosio L., Gigli N., and Savaré G. Gradient Flows in Metric Spaces and in the Wasserstein Space of Probability Measures. Lectures Math. ETH Zurich (2005), Birkhäuser, Basel
    • (2005) Lectures Math. ETH Zurich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 5
    • 0035627821 scopus 로고    scopus 로고
    • Renormalized solutions to the Vlasov equations with coefficient of bounded variations
    • Bouchut F. Renormalized solutions to the Vlasov equations with coefficient of bounded variations. Arch. Ration. Mech. Anal. 157 (2001) 75-90
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , pp. 75-90
    • Bouchut, F.1
  • 6
    • 0036487117 scopus 로고    scopus 로고
    • Uniqueness of continuous solutions for BV vector fields
    • Colombini F., and Lerner N. Uniqueness of continuous solutions for BV vector fields. Duke Math. J. 111 (2002) 357-384
    • (2002) Duke Math. J. , vol.111 , pp. 357-384
    • Colombini, F.1    Lerner, N.2
  • 7
    • 33646357997 scopus 로고    scopus 로고
    • ∞ solutions for a class of conormal BV vector fields
    • Amer. Math. Soc., Providence, RI
    • ∞ solutions for a class of conormal BV vector fields. Contemp. Math. vol. 368 (2005), Amer. Math. Soc., Providence, RI 133-156
    • (2005) Contemp. Math. , vol.368 , pp. 133-156
    • Colombini, F.1    Lerner, N.2
  • 8
    • 0002833142 scopus 로고
    • On the Fokker-Planck-Boltzmann equation
    • DiPerna R.J., and Lions P.-L. On the Fokker-Planck-Boltzmann equation. Comm. Math. Phys. 120 (1988) 1-23
    • (1988) Comm. Math. Phys. , vol.120 , pp. 1-23
    • DiPerna, R.J.1    Lions, P.-L.2
  • 9
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • DiPerna R.J., and Lions P.-L. On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Ann. of Math. 130 2 (1989) 321-366
    • (1989) Ann. of Math. , vol.130 , Issue.2 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.-L.2
  • 10
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • DiPerna R.J., and Lions P.-L. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 3 (1989) 511-547
    • (1989) Invent. Math. , vol.98 , Issue.3 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.-L.2
  • 11
    • 34447559907 scopus 로고    scopus 로고
    • Deux remarques sur les flots généralisées d'équations différentielles ordinaires
    • Hauray M., LeBris C., and Lions P.-L. Deux remarques sur les flots généralisées d'équations différentielles ordinaires (Two remarks generalized flows for ordinary differential equations). C. R. Math. Acad. Sci. Paris 344 12 (2007) 759-764
    • (2007) C. R. Math. Acad. Sci. Paris , vol.344 , Issue.12 , pp. 759-764
    • Hauray, M.1    LeBris, C.2    Lions, P.-L.3
  • 12
    • 12944260508 scopus 로고    scopus 로고
    • Strong solutions of stochastic equations with singular time dependent drift
    • Krylov N.V., and Röckner M. Strong solutions of stochastic equations with singular time dependent drift. Probab. Theory Related Fields 131 2 (2005) 154-196
    • (2005) Probab. Theory Related Fields , vol.131 , Issue.2 , pp. 154-196
    • Krylov, N.V.1    Röckner, M.2
  • 14
    • 36649013947 scopus 로고    scopus 로고
    • C. LeBris, P.-L. Lions, Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients, Comm. Partial Differential Equations, in press
  • 15
    • 36649023393 scopus 로고    scopus 로고
    • C. LeBris, P.-L. Lions, Generalized flows for stochastic differential equations with irregular coefficients, in preparation
  • 16
    • 4544270223 scopus 로고
    • Équations différentielles opérationnelles et problèmes aux limites
    • Springer-Verlag, Berlin (in French)
    • Lions J.-L. Équations différentielles opérationnelles et problèmes aux limites. Grundlehren Math. Wiss. vol. 111 (1961), Springer-Verlag, Berlin (in French)
    • (1961) Grundlehren Math. Wiss. , vol.111
    • Lions, J.-L.1
  • 17
    • 0032043481 scopus 로고    scopus 로고
    • Sur les équations différentielles ordinaires et les équations de transport
    • Lions P.-L. Sur les équations différentielles ordinaires et les équations de transport (On ordinary differential equations and transport equations). C. R. Math. Acad. Sci. Paris 326 7 (1998) 833-838
    • (1998) C. R. Math. Acad. Sci. Paris , vol.326 , Issue.7 , pp. 833-838
    • Lions, P.-L.1
  • 18
    • 0037693221 scopus 로고
    • Multidimensional Diffusion Processes
    • Springer-Verlag, Berlin
    • Stroock D.W., and Varadhan S.R.S. Multidimensional Diffusion Processes. Grundlehren Math. Wiss. vol. 233 (1979), Springer-Verlag, Berlin
    • (1979) Grundlehren Math. Wiss. , vol.233
    • Stroock, D.W.1    Varadhan, S.R.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.