Skip to main content

Rate of convergence in the Euler scheme for stochastic differential equations with non-Lipschitz diffusion and Poisson measure

We study the rate of convergence and some other properties of the Euler scheme for stochastic differential equations with non-Lipschitz diffusion and Poisson measure.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    J. C. Cox, J. E. Ingersoll, and S. A. Ross, “A theory of the term structure of interest rate,” Econometrica, 53, No. 2, 385–407 (1985).

    MathSciNet  Article  Google Scholar 

  2. 2.

    M. Bossy and A. Diop, Euler Scheme for One-Dimensional SDEs with a Diffusion Coefficient Function of the Formxα, α ∈ [1/2, 1), INRIA, Sophia-Antipolis, France (2006).

    Google Scholar 

  3. 3.

    A. Berkaoui, M. Bossy, and A. Diop, “Euler Scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence,” ESAIM: Probab. Statist., 12, 1–11 (2008).

    MathSciNet  MATH  Article  Google Scholar 

  4. 4.

    G. Deelstra and F. Delbaen, “Convergence of discretized stochastic (interest rate) process with stochastic drift term,” Appl. Stochast. Models Data Analysis, 14, No. 1, 77–84 (1998).

    MathSciNet  MATH  Article  Google Scholar 

  5. 5.

    Yu. S. Mishura and S. V. Posashkova, “The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion,” Rand. Oper. Stochast. Equat., 19, 63–89 (2011).

    Article  Google Scholar 

  6. 6.

    N. Bruti-Liberati and E. Platen, “Strong approximations of stochastic differential equations with jumps,” J. Comput. Appl. Math., 205, No. 2, 982–1001 (2007).

    MathSciNet  MATH  Article  Google Scholar 

  7. 7.

    V. P. Zubchenko and Yu. S. Mishura, “Existence and uniqueness of solutions of stochastic differential equations with non-Lipschitz diffusion and Poisson measure,” Teor. Imovir. Mat. Statist., 80, 43–54 (2009).

    MATH  Google Scholar 

  8. 8.

    V. P. Zubchenko, “Properties of solutions of stochastic differential equations with random coefficients, non-Lipschitz diffusion, and Poisson measures,” Teor. Imovir. Mat. Statist., 82, 30–42 (2010).

    MathSciNet  Google Scholar 

  9. 9.

    P. E. Protter, Stochastic Integration and Differential Equations, Springer, Berlin–Heidelberg–New York (2004).

    MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to V. P. Zubchenko.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 40–60, January, 2011.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zubchenko, V.P., Mishura, Y.S. Rate of convergence in the Euler scheme for stochastic differential equations with non-Lipschitz diffusion and Poisson measure. Ukr Math J 63, 49 (2011). https://doi.org/10.1007/s11253-011-0487-y

Download citation

Keywords

  • Interest Rate
  • Random Process
  • Stochastic Differential Equation
  • Strong Convergence
  • Wiener Process