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Volumn 82, Issue 1, 2010, Pages 53-68

Approximate mcKean-Vlasov representations for a class of sPDEs

Author keywords

Kushner stratonovitch equation; McKean vlasov equations; Non linear diffusions; Particle approximations; Stochastic partial differential equations; Zakai equation

Indexed keywords


EID: 76849109369     PISSN: 17442508     EISSN: 17442516     Source Type: Journal    
DOI: 10.1080/17442500902723575     Document Type: Article
Times cited : (97)

References (20)
  • 1
    • 76849105708 scopus 로고
    • Communication systems and random process theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977), NATO Advanced Study Inst. Ser., Ser. E: Appl. Sci., No. 25, Sijthoff & Noordhoff, Alphen aan den Rijn
    • J.M.C. Clark, The design of robust approximations to the stochastic differential equations of nonlinear filtering, Communication systems and random process theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977), pp. 721-734. NATO Advanced Study Inst. Ser., Ser. E: Appl. Sci., No. 25, Sijthoff & Noordhoff, Alphen aan den Rijn (1978).
    • (1978) The Design of Robust Approximations to the Stochastic Differential Equations of Nonlinear Filtering , pp. 721-734
    • Clark, J.M.C.1
  • 2
    • 23844437104 scopus 로고    scopus 로고
    • On a robust version of the integral representation formula of nonlinear filtering
    • J.M.C. Clark and D. Crisan, On a robust version of the integral representation formula of nonlinear filtering, Probab. Theory Relat. Fields 1 (2005), pp. 43-56.
    • (2005) Probab. Theory Relat. Fields , vol.1 , pp. 43-56
    • Clark, J.M.C.1    Crisan, D.2
  • 3
    • 0038336146 scopus 로고    scopus 로고
    • Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation
    • D. Crisan, Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation, Ann. Probab. 31(2) (2003), pp. 693-718.
    • (2003) Ann. Probab , vol.31 , Issue.2 , pp. 693-718
    • Crisan, D.1
  • 4
    • 0036504051 scopus 로고    scopus 로고
    • A survey of convergence results on particle filtering methods for practitioners
    • D. Crisan and A. Doucet, A survey of convergence results on particle filtering methods for practitioners, IEEE Trans. Signal Process. 50(3) (2002), pp. 736-746.
    • (2002) Ieee Trans. Signal Process , vol.50 , Issue.3 , pp. 736-746
    • Crisan, D.1    Doucet, A.2
  • 5
    • 0033261066 scopus 로고    scopus 로고
    • A particle approximation of the solution of the Kushner-Stratonovitch equation probab
    • D. Crisan and T. Lyons, A particle approximation of the solution of the Kushner-Stratonovitch equation Probab, Theory Relat. Fields 115(4) (1999), pp. 549-578.
    • (1999) Theory Relat. Fields , vol.115 , Issue.4 , pp. 549-578
    • Crisan, D.1    Lyons, T.2
  • 7
    • 17744362474 scopus 로고    scopus 로고
    • Interacting particle systems approximations of the Kushner- Stratonovitch equation
    • D. Crisan, P. Del Moral, and T. Lyons, Interacting particle systems approximations of the Kushner- Stratonovitch equation, Adv. Appl. Probab. 31(3) (1999), pp. 819-838.
    • (1999) Adv. Appl. Probab. , vol.31 , Issue.3 , pp. 819-838
    • Crisan, D.1    del Moral, P.2    Lyons, T.3
  • 10
    • 0007461162 scopus 로고    scopus 로고
    • A Moran particle system approximation of Feynman-Kac formulae
    • P. Del Moral and L. Miclo, A Moran particle system approximation of Feynman-Kac formulae, Stoch. Process. Appl. 86(2) (2000), pp. 193-216.
    • (2000) Stoch. Process. Appl. , vol.86 , Issue.2 , pp. 193-216
    • del Moral, P.1    Miclo, L.2
  • 11
    • 0014807437 scopus 로고
    • Likelihood functions for stochastic signals in white noise
    • T.E. Duncan, Likelihood functions for stochastic signals in white noise, Inf. Control 16 (1970), pp. 303-310.
    • (1970) Inf. Control , vol.16 , pp. 303-310
    • Duncan, T.E.1
  • 12
    • 0003248250 scopus 로고
    • Stochastic differential equations and diffusion processes
    • North-Holland Publishing Co./Kodansha, Ltd, Amsterdam-New York/Tokyo
    • N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, in North-Holland Mathematical Library, Vol. 24, North-Holland Publishing Co./Kodansha, Ltd, Amsterdam-New York/Tokyo, 1981.
    • (1981) North-Holland Mathematical Library , vol.24
    • Ikeda, N.1    Watanabe, S.2
  • 13
    • 0003242243 scopus 로고
    • Brownian motion and stochastic calculus
    • 2nd ed., Springer-Verlag, New York
    • I. Karatzas and S.E. Shreve, Brownian motion and stochastic calculus, in Graduate Texts in Mathematics, Vol. 113, 2nd ed., Springer-Verlag, New York, 1991.
    • (1991) Graduate Texts in Mathematics , vol.113
    • Karatzas, I.1    Shreve, S.E.2
  • 14
    • 0000273833 scopus 로고    scopus 로고
    • Particle representation for a class of nonlinear SPDE's
    • T.G. Kurtz and J. Xiong, Particle representation for a class of nonlinear SPDE's, Stoch. Process. Appl. 83(1) (1999), pp. 103-126.
    • (1999) Stoch. Process. Appl. , vol.83 , Issue.1 , pp. 103-126
    • Kurtz, T.G.1    Xiong, J.2
  • 16
    • 84937349138 scopus 로고
    • Stochastic optimal control with noisy observations
    • R.E. Mortensen, Stochastic optimal control with noisy observations, Int. J. Control 4(1) (1966), pp. 455-464.
    • (1966) Int. J. Control. , vol.4 , Issue.1 , pp. 455-464
    • Mortensen, R.E.1
  • 17
    • 0002064777 scopus 로고    scopus 로고
    • Filtrage Non Linéaire et Equations aux Dérivées Partielles Stochastiques Associées
    • Springer-Verlag, Berlin, Lecture Notes in Mathematics
    • E. Pardoux, Filtrage Non Linéaire et Equations aux Dérivées Partielles Stochastiques Associées, in Ecole d'Eté de Probabilités de Saint-Flour XIX - 1989, Lecture Notes in Mathematics, Vol. 1464, Springer-Verlag, Berlin, 1991.
    • Ecole D'eté De Probabilités De Saint-flour Xix - 1989 , vol.1464 , pp. 1991
    • Pardoux, E.1
  • 19
    • 0742316786 scopus 로고    scopus 로고
    • Aspects of Sobolev-type inequalities
    • Cambridge University Press, Cambridge
    • L. Saloff-Coste, Aspects of Sobolev-type inequalities, in London Mathematical Society Lecture Note Series, Vol. 289, Cambridge University Press, Cambridge, 2002.
    • (2002) London Mathematical Society Lecture Note Series , vol.289
    • Saloff-Coste, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.