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Criteria of absolute continuity of measures corresponding to multivariate point processes

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Proceedings of the Third Japan — USSR Symposium on Probability Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 550))

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References

  1. Jacod J., Multivariate point processes: predictable projection, Radon-Mikodym derivatives, representation of martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete 31 (1975), 235–253.

    Article  MathSciNet  MATH  Google Scholar 

  2. Kabanov Yu.M., Lipcer R.Š., Širyaev A.N., Martingale techniques in point processes theory. School-seminar on the theory of stochastic processes (Druskininkai 25–30 Nov., 1974), Vilnius 1975, part II, 269–354. (in Russian).

    Google Scholar 

  3. Skorokhod A.V., Random processes with independent increments, “Nauka”, Moscow, 1964.

    Google Scholar 

  4. Girsanov J.V., On transforming a certain class of stochastic processes by absolute continuous substitution of measures. Theor. Probability Appl. 5(1960), 285–307.

    Article  MathSciNet  MATH  Google Scholar 

  5. Ershov M.P., On the absolute continuity of measures corresponding to diffusion processes. Theor. Probability Appl. XVII, 1(1972), 173–178.

    Google Scholar 

  6. Lipcer R.Š., Širyaev A.N., On the absolute continuity of measures corresponding to processes of diffusion type with respect to the Wiener measure. Izv. Akad. Nauk. Ser. Mat. 36(1972), 847–889 (in Russian).

    Google Scholar 

  7. Lipcer R.Š., Širyaev A.N., Statistics of random processes, “Nauka”, Moscow, 1974. (Springer-Verlag, 1976).

    Google Scholar 

  8. Grigelionis B., On the absolute continuity of measures corresponding to stochastic processes; Litovsk. Mat. Sb.XI, 4(1971), 783–794 (in Russian).

    MathSciNet  MATH  Google Scholar 

  9. Grigelionis B. On the structure of the densities of measures corresponding to stochastic processes, Litovsk. Mat. Sb. XIII 1(1973), 71–78 (in Russian).

    MathSciNet  MATH  Google Scholar 

  10. Van Shuppen, Wong E., Transformation of local margingales under a change of low, AMS, 2, 5 (1974), 879–888.

    Google Scholar 

  11. Kailath T., Zakai M., Absolute continuity and Radon-Nikodym derivatives for certain measures relative to Wiener measure, AMS, 42, 1(1971), 130–140.

    MathSciNet  MATH  Google Scholar 

  12. Kailath T., The structure of Radon-Nikodim derivatives with respect to Wiener measure and related measures, AMS, 42(1971), 1054–1067.

    MathSciNet  MATH  Google Scholar 

  13. Segall A., Kailath T., Radon-Nikodim derivatives with respect to measures induced by discontinuous independent-increments process, Ann. Probability, 3, 3(1975), 449–464.

    Article  MathSciNet  MATH  Google Scholar 

  14. Boel R., Varaiya P., Wong E., Martingales on jump processes I, II, SIAM J. Control, 13, 5(1975), 999–1061.

    Article  MathSciNet  MATH  Google Scholar 

  15. Bremand P., The martingale theory of point processes over the real half line admitting an intensity, Lect. Notes Econ. and Math. Syst. 107(1975), 519–542.

    Article  MathSciNet  Google Scholar 

  16. Briggs, V.D., Densities for infinitely divisible random processes. J. Multivar. Analysis 5(1975), 178–205.

    Article  MathSciNet  MATH  Google Scholar 

  17. Kadota T.T., Shepp L.A., Conditions for the absolute continuity between a certain pair of probability measures, Z. Wahrscheinlichkeitstheorie verw. Gebiete 16, 3(1970), 250–260.

    Article  MathSciNet  MATH  Google Scholar 

  18. Orey S., Radon-Nikodim derivatives of probability measure: martingales methods, Dpt. Found. Math. Sc. Tokyo Univ. of Education, 1974.

    Google Scholar 

  19. Jacod J., Memin J., Characteristiques locales et conditions de continuité absolute pour les sémi-martingales (1975), to appear.

    Google Scholar 

  20. Jacod J., Un théoreme de representation pour les martingales discontinues (1975), to appear.

    Google Scholar 

  21. Dellacherie C., Capacités et processus stochastiques. Berlin, Heidelberg, New York: Springer 1972.

    MATH  Google Scholar 

  22. Gikhman J., Skorokhod A., Introduction to the theory of random processes. W.B. Saunders Co., Philadelphia.

    Google Scholar 

  23. Meyer P.A., Probability and potential. Waltham: Blaisdell, 1966.

    Google Scholar 

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Authors and Affiliations

  1. Steklov Mathematical Institute, Academy of Sciences of the USSR, Moscow

    Yu. M. Kabanov, R. S. Lipcer & A. N. Širyaev

Authors
  1. Yu. M. Kabanov
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  2. R. S. Lipcer
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  3. A. N. Širyaev
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Editor information

Gisiro Maruyama Jurii V. Prokhorov

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© 1976 Springer-Verlag

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Kabanov, Y.M., Lipcer, R.S., Širyaev, A.N. (1976). Criteria of absolute continuity of measures corresponding to multivariate point processes. In: Maruyama, G., Prokhorov, J.V. (eds) Proceedings of the Third Japan — USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077493

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  • DOI: https://doi.org/10.1007/BFb0077493

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07995-8

  • Online ISBN: 978-3-540-37966-9

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