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White noise calculus for two-parameter filtering

  • Infinite-dimensional Stochastic Systems And Random Fields. Stochastic Partial Differential Equations
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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 96))

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References

  1. R. Cairoli, Sur une équation différentielle stochastique, C.R.Acad. Paris, t.274, Série, 1739–1742 (1972).

    Google Scholar 

  2. G. Kallianpur and R.L. Karandikar, White noise calculus and nonlinear filtering theory, The Ann. Probability, 13(4), 1033–1107 (1985).

    Google Scholar 

  3. G. Kallianpur and R.L. Karandikar, Measure-valued equations for the optimum filter in finitely additive nonlinear filtering theory, Z.Wahrsch.Verw.Geb. 66, 1–17 (1984).

    Google Scholar 

  4. H. Korezlioglu, Passage from two-parameters to infinite dimension, to be published in "Stochastic Partial Differential Equations", Trento Meeting, sept.30–oct.5, 1985, Lect. Notes in Math. Springer-Verlag.

    Google Scholar 

  5. H. Korezlioglu, P. Lefort and G. Mazziotto, Une propriété markovienne et diffusions associées, Lect. Notes in Math. 863, 245–274, Springer-Verlag (1981).

    Google Scholar 

  6. H. Korezlioglu and G.Mazziotto, Approximation of the nonlinear filter by periodic sampling and quantization, Lect. Notes Control and Inf. Sciences, 62, Springer-Verlag (1984).

    Google Scholar 

  7. H. Korezlioglu, G. Mazziotto and J. Szprirglas, Nonlinear filtering equations for two-parameter semimartingales, Stochastic Process. Applications 15, 139–269 (1983).

    Google Scholar 

  8. R. Mazumdar and A. Bagchi, A finitely additive white noise approach to filtering for two-parameter diffusion processes, in "Theory and Applications in Nonlinear Control Systems", North Holland (1986).

    Google Scholar 

  9. D. Nualart, Two-parameter diffusion processes and martingales, Stochastic Process. Applications 15, 31–54 (1983).

    Google Scholar 

  10. E. Wong, Recursive causal linear filtering for two-dimensional random fields, IEEE Trans. IT 24(1), 50–59 (1978).

    Google Scholar 

  11. E. Wong and E.T. Tsui, One-sided recursive filters for two-dimensional random fields, IEEE Trans. IT 23(5), 633–637 (1977).

    Google Scholar 

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Hans Jürgen Engelbert Wolfgang Schmidt

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© 1987 Springer-Verlag

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Kallianpur, G., Korezlioglu, H. (1987). White noise calculus for two-parameter filtering. In: Engelbert, H.J., Schmidt, W. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 96. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038922

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  • DOI: https://doi.org/10.1007/BFb0038922

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18010-4

  • Online ISBN: 978-3-540-47245-2

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