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Volumn 8, Issue 3, 2008, Pages 543-560

A problem in stochastic averaging of nonlinear filters

Author keywords

Homogenization; Nonlinear filtering; Stochastic partial differential equations

Indexed keywords


EID: 56549127222     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493708002445     Document Type: Conference Paper
Times cited : (14)

References (21)
  • 1
    • 22144450768 scopus 로고
    • Homogenization of a class of stochastic partial differential equations
    • Birkhäuser
    • A. Bensoussan, Homogenization of a class of stochastic partial differential equations, in Progress in Nonlinear Differential Equations Application, Vol. 5 (Birkhäuser, 1991), pp. 47-65.
    • (1991) Progress in Nonlinear Differential Equations Application , vol.5 , pp. 47-65
    • Bensoussan, A.1
  • 2
    • 0342917099 scopus 로고
    • Nonlinear filtering with homogenization
    • A. Bensoussan and G. L. Blankenship, Nonlinear filtering with homogenization, Stoch. 17 (1986) 67-90.
    • (1986) Stoch , vol.17 , pp. 67-90
    • Bensoussan, A.1    Blankenship, G.L.2
  • 4
    • 21344437201 scopus 로고
    • Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
    • A. G. Bhatt, G. Kallianpur and R. L. Karandikar, Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering, Ann. Probab. 23 (1995) 1895-1938.
    • (1995) Ann. Probab , vol.23 , pp. 1895-1938
    • Bhatt, A.G.1    Kallianpur, G.2    Karandikar, R.L.3
  • 6
    • 84971110219 scopus 로고
    • The perturbed test function method for viscosity solutions of nonlinear PDE
    • L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 359-375.
    • (1989) Proc. Roy. Soc. Edinburgh Sect. A , vol.111 , pp. 359-375
    • Evans, L.C.1
  • 7
    • 0032362579 scopus 로고    scopus 로고
    • Random perturbations of nonlinear oscillators
    • M. Freidlin and M. Weber, Random perturbations of nonlinear oscillators, Ann. Probab. 26 (1998) 925-967.
    • (1998) Ann. Probab , vol.26 , pp. 925-967
    • Freidlin, M.1    Weber, M.2
  • 8
    • 0026867441 scopus 로고
    • Convergence of filters with application to the Kalman-Bucy case
    • E. M. Goggin, Convergence of filters with application to the Kalman-Bucy case, IEEE Trans. Inform. Th. 38 (1992) 1091-1100.
    • (1992) IEEE Trans. Inform. Th , vol.38 , pp. 1091-1100
    • Goggin, E.M.1
  • 9
    • 0001659363 scopus 로고
    • Convergence in distribution of conditional expectation
    • E. M. Goggin, Convergence in distribution of conditional expectation, Ann. Probab. 22 (1994) 1097-1114.
    • (1994) Ann. Probab , vol.22 , pp. 1097-1114
    • Goggin, E.M.1
  • 10
    • 0005495507 scopus 로고
    • A limit theorem for solutions of differential equations with a random right hand part
    • R. Z. Has'minskiǐ, A limit theorem for solutions of differential equations with a random right hand part, Teor. Verojatnost. i Primenen 11 (1966) 444-462.
    • (1966) Teor. Verojatnost. i Primenen , vol.11 , pp. 444-462
    • Has'minskiǐ, R.Z.1
  • 11
    • 22144467454 scopus 로고    scopus 로고
    • Homogenization problem for stochastic partial differential equations of Zakai type
    • N. Ichihara, Homogenization problem for stochastic partial differential equations of Zakai type, Stoch. Stoch. Rep. 76 (2004) 243-266.
    • (2004) Stoch. Stoch. Rep , vol.76 , pp. 243-266
    • Ichihara, N.1
  • 12
    • 22144487716 scopus 로고    scopus 로고
    • Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback
    • N. Ichihara, Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback, J. Math. Soc. Jpn. 57 (2005) 593-603.
    • (2005) J. Math. Soc. Jpn , vol.57 , pp. 593-603
    • Ichihara, N.1
  • 16
    • 0001157746 scopus 로고
    • On the differential equations satisfied by conditional probability densities of Markov processes
    • H. J. Kushner, On the differential equations satisfied by conditional probability densities of Markov processes, SIAM J. Control 2 (1964) 106-119.
    • (1964) SIAM J. Control , vol.2 , pp. 106-119
    • Kushner, H.J.1
  • 18
    • 0142059896 scopus 로고    scopus 로고
    • Convergence of nonlinear filters for randomly perturbed dynamical systems
    • V. M. Lucic and A. J. Heunis, Convergence of nonlinear filters for randomly perturbed dynamical systems, Appl. Math. Optim. 48 (2003) 93-128.
    • (2003) Appl. Math. Optim , vol.48 , pp. 93-128
    • Lucic, V.M.1    Heunis, A.J.2
  • 19
    • 0010398784 scopus 로고
    • Martingale approach to some limit theorems
    • Papers from the Duke Turbulence Conference Duke Univ, Durham, N.C, Paper No. 6, Duke Univ
    • G. C. Papanicolaou, D. Stroock and S. R. S. Varadhan, Martingale approach to some limit theorems, in Papers from the Duke Turbulence Conference (Duke Univ., Durham, N.C., 1976), Paper No. 6, Duke Univ. Math. Ser., Vol. III. (Duke Univ., 1977).
    • (1976) Duke Univ. Math. Ser , vol.3
    • Papanicolaou, G.C.1    Stroock, D.2    Varadhan, S.R.S.3
  • 20
    • 56549104334 scopus 로고    scopus 로고
    • B. L. Rozovskiǐ, Stochastic Evolution Systems, Mathematics and its Applications (Soviet Series), 35 [Linear theory and applications to nonlinear filtering, Translated from Russian by A. Yarkho] (Kluwer, 1990).
    • B. L. Rozovskiǐ, Stochastic Evolution Systems, Mathematics and its Applications (Soviet Series), Vol. 35 [Linear theory and applications to nonlinear filtering, Translated from Russian by A. Yarkho] (Kluwer, 1990).
  • 21
    • 0001702452 scopus 로고
    • On the optimal filtering of diffusion processes
    • M. Zakai, On the optimal filtering of diffusion processes, Z. Wahr. Verw. Gebiete 11 (1969) 230-243.
    • (1969) Z. Wahr. Verw. Gebiete , vol.11 , pp. 230-243
    • Zakai, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.