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Approximation of stochastic differential equations and application of the stochastic calculus of variations to the rate of convergence

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Stochastic Analysis and Related Topics

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References

  1. H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. Henri Poincaré, Section B, 13 (1977), 99–125.

    MathSciNet  MATH  Google Scholar 

  2. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland, 1981.

    Google Scholar 

  3. H. Kunita, Convergence of stochastic flows connected with stochastic ordinary differential equations, Stochastics 17 (1986), 215–251.

    Article  MathSciNet  MATH  Google Scholar 

  4. V. Mackevičius, On the support of the solution of the stochastic differential equation (in Russian), Lietuvos Mat. Rinkinys 26 (1986), 91–98.

    Google Scholar 

  5. V. Mackevičius, S p stabilité des solutions d'équations différentielles stochastiques symétriques avec semi-martingales directrices discontinues, C. R. Acad. Sc. Paris, Série I, 19 (1986), 689–692.

    Google Scholar 

  6. V. Mackevičius, S p stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales, to appear.

    Google Scholar 

  7. D. Nualart, Non causal stochastic integrals and calculus, this volume.

    Google Scholar 

  8. D. Ocone, A guide to the stochastic calculus of variations, this volume.

    Google Scholar 

  9. M. Pontier and J. Szpirglas, Convergence des approximations de Mc Shane d'une diffusion sur une variété compacte, Séminaire de Probabilités, to appear.

    Google Scholar 

  10. A.V. Skorohod, On a generalization of a stochastic integral, Theory Proba. Applications 20 (1975), 219–233.

    Article  MathSciNet  Google Scholar 

  11. H.J. Sussmann, On the gap between deterministic and stochastic ordinary differential equations, Annals Proba. 6 (1978), 19–41.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Talay, Analyse numérique des équations différentielles stochastiques, Thèse de 3ème cycle, Université de Provence, 1982.

    Google Scholar 

  13. Y. Yamato, Stochastic differential equations and nilpotent Lie algebras, Z. Wahrschein. verw. G. 47 (1979), 213–229.

    Article  MathSciNet  MATH  Google Scholar 

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Hayri Korezlioglu Ali Süleyman Ustunel

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© 1988 Springer-Verlag

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Picard, J. (1988). Approximation of stochastic differential equations and application of the stochastic calculus of variations to the rate of convergence. In: Korezlioglu, H., Ustunel, A.S. (eds) Stochastic Analysis and Related Topics. Lecture Notes in Mathematics, vol 1316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081935

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  • DOI: https://doi.org/10.1007/BFb0081935

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19315-9

  • Online ISBN: 978-3-540-39186-9

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