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Weak and strong solutions of stochastic differential equations: Existence and stability

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Stochastic Integrals

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References

  1. A. BENSOUSSAN, R. TEMAM: Equations aux dérivées partielles stochastiques non linéaires. Israël J. Math. 11, 1972, 95–129.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. BILLINGSLEY: Convergence of probability measures. Wiley and Sons: New-York, 1968.

    MATH  Google Scholar 

  3. C. DOLEANS-DADE: On the existence and unicity of solution of stochastic integral equations. Z. für Wahr. 34, 93–101, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. DOLEANS-DADE, P.A. MEYER: Equations différentielles stochastiques. Sém. Probab. XI, Lect. Notes in Math. 581, 376–382, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. EMERY: Une topologie sur l'espace des seminartingales. Sém. Probab. XIII, Lect. Notes in Math. 721, 260–281, 1979.

    Article  MathSciNet  Google Scholar 

  6. M. EMERY: Equations différentielles stochastiques lipschitziennes: étude de la stabilité. Sém. Probab. XIII, Lect. Notes in Math. 721 281–293, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  7. B. GRIGELIONIS, R. MIKULEVICIUS: On weak convergence of semimartingales. Lit. Math. J. XXI, 1981.

    Google Scholar 

  8. I. GYONGY, N.V. KRYLOV: On stochastic equations with respect to semimartingales I, to appear, 1980.

    Google Scholar 

  9. J. JACOD: Calcul stochastique et problèmes de martingales. Lect. Notes in Math. 714, Springer Verlag: Berlin, 1979.

    MATH  Google Scholar 

  10. J. JACOD: Intégrales stochastiques par rapport à une semimartingale vectorielle et changements de filtration. Sém. Probab. XIV, Lect. Notes in Math. 784, 161–172, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. JACOD: Weak and strong solutions of stochastic differential equations. Stochastics, 3, 171–191, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. JACOD: Une condition d'existence et d'unicité pour les solutions fortes d'équations différentielles stochastiques. To appear in Stochastics, 1980.

    Google Scholar 

  13. J. JACOD, J. MEMIN: Existence of weak solutions for stochastic differential equations driven by semimartingales. To appear in Stochastics, 1980.

    Google Scholar 

  14. J. JACOD, J. MEMIN, M. METIVIER: Tightness and stopping times: some new conditions. To appear, 1980.

    Google Scholar 

  15. J. JACOD, J. MEMIN: Sur un type de convergence intermédiaire entre la convergence en probabilité et la convergence en loi. To appear in: Sém. de Probab. XV, 1980.

    Google Scholar 

  16. V.A. LEBEDEV: On the existence of a solution of the stochastic equation with respect to a martingale and a stochastic measure. Int. Symp. on Stoch. Diff. Equa., Vilnius, 65–69, 1978.

    Google Scholar 

  17. J. MEMIN: Espaces de semimartingales et changements de probabilité. Z. für Wahr. 52, 9–40, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  18. M. METIVIER, J. PELLAUMAIL: Stochastic integration. To appear, 1980.

    Google Scholar 

  19. M. METIVIER, G. PISTONE: Sur une équation d'évolution stochastique. Bull. Soc. Math. France, 104, 65–85, 1976.

    MathSciNet  MATH  Google Scholar 

  20. P.A. MEYER: Un cours sur les intégrales stochastiques. Sém. Probab. X, Lect. Notes in Math. 511, 245–400, 1976.

    Article  MATH  Google Scholar 

  21. P.A. MEYER: Conergence faible et compacité des temps d'arrêt d'après Baxter et Chacon. Sém. Probab. XII, Lect. Notes in Math. 649, 411–423, 1978.

    Article  MATH  Google Scholar 

  22. E. PARDOUX: Thèse, Univ. Paris-Sud, 1975.

    Google Scholar 

  23. J. PELLAUMAIL: Solutions faibles pour des processus discontinus. Comptes Rendus Acad. Sci. Paris (A) 290, 431–433, 1980.

    MathSciNet  MATH  Google Scholar 

  24. P. PROTTER: On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic differential equations. Ann. Probab. 5, 243–261, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  25. B.L. ROZOVSKII: A note on strong solutions of stochastic differential equations with random coefficients. To appear: 1980.

    Google Scholar 

  26. A.V. SKOROKHOD: Limit theorems for stochastic processes. Theor. Probab. and Appl. 1, 261–290 (AMS Transl.) 1956.

    Article  MathSciNet  MATH  Google Scholar 

  27. C. STRICKER: Quasimartingales, martingales locales, semimartingales et filtrations. Z. für Wahr. 39, 55–63, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  28. D.W. STROOCK, S.R.S. VARADHAN: Multidimensional diffusion processes. Springer Verlag: Berlin, 1979.

    MATH  Google Scholar 

  29. T. YAMADA, S. WATANABE: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11, 156–167, 1971.

    MATH  Google Scholar 

  30. A. V. ZVONKIN, N.V. KRYLOV: On strong solutions of stochastic differential equations. School-Seminar (Druskininkai), Vilnius, Ac. Sci. Lit. SSR, II, 9–88, 1975.

    MathSciNet  Google Scholar 

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David Williams

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© 1981 Springer-Verlag

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Jacod, J., Memin, J. (1981). Weak and strong solutions of stochastic differential equations: Existence and stability. In: Williams, D. (eds) Stochastic Integrals. Lecture Notes in Mathematics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088728

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  • DOI: https://doi.org/10.1007/BFb0088728

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