Skip to main content
Log in

Convergence of solutions of backward stochastic equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

We establish conditions for the weak convergence of solutions of backward stochastic equations in the case of the weak convergence of coefficients.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. L. Kamynin, “Limit transition in quasilinear parabolic equations with weakly convergent coefficients and the asymptotic behavior of solutions of the Cauchy problem,” Mat. Sb., 181, 1031–1047 (1990).

    Google Scholar 

  2. S. N. Kruzhkov and V. L. Kamynin, “On limit transition in quasilinear parabolic equations,” Tr. Mat. Inst. Akad. Nauk SSSR, 167, 183–206 (1985).

    MathSciNet  MATH  Google Scholar 

  3. S. Pardoux and S. Peng, “Adapted solution of backward stochastic differential equation,” Syst. Contr. Lett., 14, 55–61 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  4. S. N. Kruzhkov, “Quasilinear parabolic equations and systems with two independent variables,” Tr. Sem. im. Petrovskogo, 5, 217–272 (1979).

    MathSciNet  MATH  Google Scholar 

  5. S. Ya. Makhno, “Convergence of diffusion processes,” Ukr. Mat. Zh., 44, No. 2, 284–289 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer, New York (1979).

    MATH  Google Scholar 

  7. P. Meyer and W. A. Zheng, “Tightness criteria for laws of semimartingales,” Ann. Inst. H. Poincaré B, 20, 353–372 (1984).

    MathSciNet  MATH  Google Scholar 

  8. N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  9. I. A. Erisova, “Convergence of solutions of backward stochastic equations,” Tr. Inst. Prikl. Mat. Mekh. Nats. Akad. Nauk Ukr., 13, 72–82 (2006).

    MathSciNet  MATH  Google Scholar 

  10. I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Vol. 3, Nauka, Moscow (1975).

    MATH  Google Scholar 

  11. N. V. Krylov, “On equations of minimax type in the theory of elliptic and parabolic equations on a plane,” Mat. Sb., 81, 3–22 (1980).

    Google Scholar 

  12. Yu. A. Alkhutov and I. T. Mamedov, “First boundary-value problem for nondivergence parabolic equations of the second order with discontinuous coefficients,” Mat. Sb., 131, 477–500 (1986).

    Google Scholar 

  13. S. Ya. Makhno, “Convergence of diffusion processes. II,” Ukr. Mat. Zh., 44, 1389–1395 (1992).

    MathSciNet  MATH  Google Scholar 

  14. E. Pardoux, “BSDE’s weak convergence and homogenization of semilinear PDE,” in: F. H. Clarke et al. (editors), Nonlinear Analysis, Differential Equations and Control, Vol. 528 (1999), pp. 503–549.

  15. R. Buckhadan, H. J. Engelbert, and A. Rascanu, “On weak solutions of backward stochastic differential equations,” Theory Probab. Appl., 49, 70–107 (2004).

    Google Scholar 

  16. E. Pardoux, “Homogenization of linear and semilinear second-order parabolic PDE with periodic coefficients: a probabilistic approach,” J. Funct. Anal., 167, 496–520 (1999).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 922–938, July, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Erisova, I.A. Convergence of solutions of backward stochastic equations. Ukr Math J 61, 1093–1112 (2009). https://doi.org/10.1007/s11253-009-0261-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0261-6

Keywords

Navigation