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The martingale calculus and applications

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 16))

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References

  1. DAVIS, M.H.A. and ELLIOTT, R.J. Optimal Control of a jump process. Zeits für Wahrs. 40, 183–202 (1977).

    Google Scholar 

  2. DAVIS, M.H.A. and VARAIYA, P. Dynamic programming conditions for partially observable systems. S.I.A.M. Jour. Control 11, 226–261 (1973).

    Google Scholar 

  3. DELLACHERIE, C. Capacités et processus stochastiques. Berlin-Heidelberg-New York. Springer 1972.

    Google Scholar 

  4. DOLEANS-DADE, C. Quelques applications de la formule de changement de variables pour les semimartingales, Zeits. für Wahrs. 16, 181–190 (1970).

    Google Scholar 

  5. ELLIOTT, R.J. A stochastic minimum principle, Bull. Amer. Math Soc. 82, 944–946 (1976).

    Google Scholar 

  6. ELLIOTT, R.J. The optimal control of a semimartingale. Proceedings of the Third Kingston Conference on Differential Games and Control Theory. To be published by M. Dekker, New York.

    Google Scholar 

  7. JACOD, J. Multivariate point processes, predictable projections, Radon-Nikodym derivatives, representation of martingales. Zeits für Wahrs 31. 235–253 (1975).

    Google Scholar 

  8. JACOD, J. Un théorème de représentation pour les martingales discontinus. Zeits für Wahrs 34, 225–245 (1976).

    Google Scholar 

  9. JACOD, J. Sur la construction des integrales stochastiques et les sousespaces stables de martingales. Sem. Prob. Stasbourg Xl. Lecture Notes in Math. 581. Springer-Verlag, Berlin-Heidelberg-New York. 1977.

    Google Scholar 

  10. JACOD, J. A general theorem of representation for martingales. Proceedings of Symposia on Pure Mathematics, Vol. 31, American Math. Society, Providence R.I. 1977.

    Google Scholar 

  11. JACOD, J. and MEMIN, J. Caractéristiques locales et conditions de continuité absolue pourles semi-martingales. Zeits für Wahrs. 35, 1–37 (1976).

    Google Scholar 

  12. JACOD, J. and YOR, M. Etude des solutions extrémales et représentation intégrale de solutions pour certains problèmes de martingales. Zeits für Wahrs. 38, 83–125 (1977).

    Google Scholar 

  13. LOEVE. M. Probability theory, 3rd. Ed. Van Nostrand. Princeton 1963.

    Google Scholar 

  14. MEYER, P. A. Un cours sur le intégrales stochastiques. Sem. Prob. Strasbourg X. Lecture Notes in Math. 511 Springer-Verlag. Berlin-Heidelberg-New York.1976.

    Google Scholar 

  15. STRIEBEL, C. Martingale conditions for the optimal control of continuous time stochastic systems. International Workshop on Stochastic Filtering and Control, Los Angeles, May 1974.

    Google Scholar 

  16. YOEURP, C. Decompositions des martingales locales et formules exponentielles. Sem. Prob. Strasbourg X. Lecture Notes in Math. 511. Springer-Verlag Berlin-Heidelberg-New York. 1976.

    Google Scholar 

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M. Kohlmann W. Vogel

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© 1979 Springer-Verlag

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Elliott, R.J. (1979). The martingale calculus and applications. In: Kohlmann, M., Vogel, W. (eds) Stochastic Control Theory and Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009379

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  • DOI: https://doi.org/10.1007/BFb0009379

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09480-7

  • Online ISBN: 978-3-540-35211-2

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