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On approximation of stochastic differential equations with coefficients depending on the past

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References

  1. V. Bally, Approximation for the solutions of stochastic differential equations. I:L p-convergence,Lect. Notes in Math. (Séminaire de Probabilités XV),850, 118–141 (1981).

    Google Scholar 

  2. M. Emery, Equations différentielles stochastiques lipschitziennes: étude de la stabilité,Lect. Notes in Math. (Séminaire de Probabilités XIII),721, 281–293 (1979).

    MATH  MathSciNet  Google Scholar 

  3. I. Gyöngy, On the approximation of stochastic differential equations,Stochastics,23, 331–352 (1988).

    MATH  MathSciNet  Google Scholar 

  4. I. Gyöngy, On approximation of stochastic Itô equations,Math. USSR Sb.,181, 743–750 (1990).

    MATH  Google Scholar 

  5. I. Gyöngy and T. Pröhle, On the approximation of stochastic differential equation and on Stroock-Varadhan's support theorem,Computers Math. Appl.,19, 65–70 (1990).

    Article  MATH  Google Scholar 

  6. B. Grigelionis and R. Mikulevičius, Stochastic evolution equations and densities of the conditional distributions,Lect. Notes in Control and Inf. Sci.,49, 49–88 (1984).

    Google Scholar 

  7. K. Itô and M. Nisio, On stationary solutions of a stochastic differential equation,J. Math. Kyoto Univ.,4, 1–75 (1964).

    MATH  MathSciNet  Google Scholar 

  8. A. Jakubowski, J. Mémin, and G. Pagès, Convergence en loi des suites d'intégrales stochastiques sur l'espaceD de Skorokhod,Probab. Theory Relat. Fields,81, 111–137 (1989).

    Article  MATH  Google Scholar 

  9. H. Kunita, Some extensions of Itô's formula,Lect. Notes in Math. (Séminaire de Probabilitès XV),850, 118–141 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms,Lect. Notes in Math. (Ecole d'Eté de Probabilités de Saint-Flour, XII-1982),1097, 143–303 (1984).

    MATH  MathSciNet  Google Scholar 

  11. V. Mackevičius,S p stability of solutions of symmetric stochastic differential equations,Lith. Math. J.,25, 343–352 (1985).

    Article  MATH  Google Scholar 

  12. V. Mackevičius,S p stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales.Ann. Inst. Henri Poincaré,23, 575–592 (1987).

    MATH  Google Scholar 

  13. J. Picard, Convergence in probability for perturbed stochastic integral equations,Probab. Theory Relat. Fields,81, 383–452 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  14. P. Protter, Approximations of solutions of stochastic differential equations driven by semimartingales,Ann. Probab.,13, 716–743 (1985).

    MATH  MathSciNet  Google Scholar 

  15. P. Protter,Stochastic Integration and Differential Equations: A New Approach, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo (Applications in Mathematics, v. 21) (1990).

    MATH  Google Scholar 

  16. R.-Q. Wu and X. Mao, Existence and uniqueness of the solutions of stochastic differential equations,Stochastics,11, 19–32 (1983).

    MATH  MathSciNet  Google Scholar 

  17. J.-A. Yan, Sur une équation différentielle stochastique générale,Lect. Notes in Math. (Séminaire de Probabilités XIV),784, 305–315 (1980).

    MATH  Google Scholar 

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Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 285–298, April–June, 1992.

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Mackevičius, V. On approximation of stochastic differential equations with coefficients depending on the past. Lith Math J 32, 227–237 (1992). https://doi.org/10.1007/BF02450421

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