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Stochastic non linear filtering equations and semimartingales

I. Main Lectures

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 972)

Keywords

  • Point Process
  • Stochastic Differential Equation
  • Stochastic Equation
  • Stochastic Partial Differential Equation
  • Local Martingale

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References

  1. J. Jacod, Calcul stochastique et problems de martingales. Lecture Notes in Math., 714, Springer-Verlag, 1979.

    Google Scholar 

  2. M. Fujisaki, G. Kallianpur, H. Kunita, Stochastic differential equations for non linear filtering problem. Osaka J. Math., 1972, Vol. 9, No 1, p. 19–40.

    MathSciNet  MATH  Google Scholar 

  3. B. Grigelionis, On stochastic non linear filtering equations of stochastic processes. Liet. matem. rinkinys, 1972, t. XII, No 4, pp. 37–51.

    MathSciNet  Google Scholar 

  4. B. Grigelionis, A martingale approach to the statistical problems of point processes. Scand. J. Statist., 1980, vol. 7, No 4, p. 190–196.

    MathSciNet  MATH  Google Scholar 

  5. M. Zakai, On the optimal filtering of diffusion processes. Z. Wahrschein. verw. Geb., 1969, vol. 11, s. 230–243.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. R.S. Liptser, A.N. Shiryaev, Statistics of random processes, I, II. Springer, 1977.

    Google Scholar 

  7. G. Kallianpur, Non linear filtering. Springer Verlag, 1980.

    Google Scholar 

  8. B. Grigelionis, R. Mikulevicius, On statistical problems of stochastic processes with penetrable boundaries, Proc. VI Intern. Conf. Math. Statist., Wisla, Poland, Lecture Notes in Statist., 2, Springer, 1980.

    Google Scholar 

  9. J. Szpirglas, G. Mazziotto, Modele general de filtrage non lineaire et equations differentielles stochastiques associées. C.R. Acad. Sci. Paris, Ser. A, 1978, vol. 286, p. 1067–1070.

    MathSciNet  MATH  Google Scholar 

  10. J. van Schupper, Stochastic filtering theory: a discussion of concepts, methods and results, Stochastic control theory and stochastic differential systems. Lecture Notes in Control and Inform. Sciences, vol. 16, Springer Verlag, 1979, p. 209–226.

    CrossRef  Google Scholar 

  11. L.G. Vetrov, On linearization of stochastic differential equations of optimal non-linear filtering. Theory Probab. Appl., 1980, vol. XXV, No 2, p. 399–407.

    MathSciNet  MATH  Google Scholar 

  12. J.M.C. Clark, The design of robust approximations to the stochastic differential equations of nonlinear filtering, in "Communication systems and random process theory", ed. J.K. Skwirzynski, Sijthoff and Noordhoff, 1978.

    Google Scholar 

  13. H.J. Kushner, A robust discrete state approximation to the optimal nonlinear filter for a diffusion. Stochastics, 1979, vol. 3, p. 75–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M.H.A. Davis, On a multiplicative functional transformation arising in nonlinear filtering theory. Z. Wahrschein. verw. Geb., 1980, vol. 54, s. 125–139.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. S.I. Marcus, Modelling and approximation of stochastic differential equations driven by semimartingales. Stochastics, 1981, vol. 4, No 3, p. 223–245.

    CrossRef  Google Scholar 

  16. R.J. Elliott, M. Kohlmann, Robust filtering for correlated multidimensional observations (preprint), 1980.

    Google Scholar 

  17. N.V. Krylov, B.L. Rozovskii, On the Cauchy problem for linear stochastic partial differential equations. Math. USSR Izvestija, 1977, vol. 11, p. 1267–1284.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. N.V. Krylov, B.L. Rozovskii, On conditional distributions of diffusion processes. Math. USSR Izvestija, 1978, vol. 12, p. 336–356.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes. Stochastics, 1979, vol. 3, p. 127–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. E. Tinfavicius, On the conditional distributions of discontinuous processes. I, II. Lietuvos matem. rinkinys, 1980, vol. XX, No 1, p. 175–191, No 4, p.187–199.

    Google Scholar 

  21. D. Michel, Regularité de lois conditionnelles en théorie du filtrage non linéaire. C.R. Acad. Sc. Paris, 1980, t. 290, ser. A, p. 387.

    MATH  Google Scholar 

  22. H. Kunita, Densities of measure — valued process governed by a stochastic partial differential equation (preprint), 1981.

    Google Scholar 

  23. B.Grigelionis, R. Milulevicius, On stochastic processes with penetrable boundaries. Liet. matem. rinkinys, 1980, t. XX, Nr. 2.

    Google Scholar 

  24. B. Grigelionis, On the representation of integer-valued random measure by means of stochastic integrals with respect to the Poisson measure. Liet. matem. rink. 1971, vol. 11, p. 93–108.

    MathSciNet  MATH  Google Scholar 

  25. B. Grigelionis, On statistical problems of stochastic processes with boundary conditions. Liet. matem. rink., 1976, t. XVI, No 1, p. 63–87.

    MathSciNet  MATH  Google Scholar 

  26. B. Grigelionis, On the reduced stochastic equations for non linear filtering of random processes. Liet. matem. rink., t. XVI, 3 (1976), 51–63.

    MathSciNet  MATH  Google Scholar 

  27. M. Metivier, J. Pellaumail, Stochastic integration. Academic Press, 1980.

    Google Scholar 

  28. I. Gyöngy, N.V. Krylov, On stochastic equations with respect to semimartingales II, Ito formula in Banach spaces. Stochastics (in print), 1981.

    Google Scholar 

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© 1982 Spring-Verlag

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Grigelionis, B. (1982). Stochastic non linear filtering equations and semimartingales. In: Mitter, S.K., Moro, A. (eds) Nonlinear Filtering and Stochastic Control. Lecture Notes in Mathematics, vol 972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064860

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  • DOI: https://doi.org/10.1007/BFb0064860

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