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Weak convergence of stochastic integrals and differential equations

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1627)

Keywords

  • Stochastic Differential Equation
  • Weak Convergence
  • Polish Space
  • Variable Formula
  • Quadratic Variation

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References

  1. Ahn, H., Protter, P., “A Remark on Stochastic Integration”, Sém. de Proba. XXVII, LNM 1583, 312–315 (1994).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Dellacherie, C., Capacités et Processus Stochastiques, Springer, Berlin (1972).

    MATH  Google Scholar 

  3. Duffie, D., Protter, P., “From discrete to continuous time finance: weak convergence of the financial gain process”, J. Math. Finance 2, 1–15 (1992).

    CrossRef  MATH  Google Scholar 

  4. Emery, M., “On the Azéma Martingales”, Sém. de Proba. XXIII, LNM 1372, 66–87 (1989).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Ethier, S., Kurtz, T. G., Markov Processes: Characterization and Convergence, Wiley, New York (1986).

    CrossRef  MATH  Google Scholar 

  6. Jacod, J., “Theoremes Limites pour les Processus”, Ecole d'Eté de Proba. de St. Flour XIII, LNM 1117, 299–409 (1985).

    MathSciNet  MATH  Google Scholar 

  7. Jacod, J., Protter, P., “A Remark on the Weak Convergence of Processes in the Skorohod Topology”, J. Theoretical Probability 6, 463–472 (1993).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Jacod, J., Shiryaev, A. N., Limit Theorems for Stochastic Processes, Springer, Berlin (1987).

    CrossRef  MATH  Google Scholar 

  9. Jakubowski, A., Mémin, J., Pagès, G., “Convergence en Loi des Suites d'Intégrales Stochastiques sur l'Espace D1 de Skorohod”, Proba. Th. Rel. Fields 81, 111–137 (1989).

    CrossRef  MATH  Google Scholar 

  10. Kurtz, T. G., Protter, P., “Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations”, Ann. Proba. 19, 1035–1070 (1991).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Kurtz, T. G., Protter, P., “Characterizing the Weak Convergence of Stochastic Integrals”, in Stochastic Analysis (M. Barlow and N. Bingham, eds.), Cambridge U. P., 255–259 (1991).

    Google Scholar 

  12. Kurtz, T. G., Protter, P., “Wong-Zakai, Corrections, Random Evolutions, and Numerical Schemes for SDEs”, in Stochastic Analysis, Academic Press, 331–346 (1991).

    Google Scholar 

  13. Mémin, M., Slominski, L., “Condition UT et Stabilité en Loi des Solutions d'Equations Différentielles Stochastiques”, Sém. de Proba. XXV, LNM 1485, 162–177 (1991).

    CrossRef  MATH  Google Scholar 

  14. Pratelli, M., “La Classe des Seminartingales qui Permettent d'Intégrer les Processus Optionnels”, Sém. de Proba. XVII, LNM 986, 311–320 (1983).

    MathSciNet  MATH  Google Scholar 

  15. Protter, P., Stochastic Integration and Differential Equations, Springer, Berlin (1990).

    CrossRef  MATH  Google Scholar 

  16. Slominski, L., “Stability of Strong Solutions of Stochastic Differential Equations”, Stoch. Processes and Their Appl. 31, 173–202 (1989).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1996 Springer-Verlag

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Kurtz, T.G., Protter, P.E. (1996). Weak convergence of stochastic integrals and differential equations. In: Talay, D., Tubaro, L. (eds) Probabilistic Models for Nonlinear Partial Differential Equations. Lecture Notes in Mathematics, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093176

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  • DOI: https://doi.org/10.1007/BFb0093176

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  • Online ISBN: 978-3-540-68513-5

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