Skip to main content
SpringerLink
Log in

Convergence of diffusion processes

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For stochastic diffusion equations with coefficients depending on a parameter, necessary and sufficient conditions of the weak convergence of solutions to the solution of a stochastic diffusion equation are obtained.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. R. Sh. Liptser and A. N. Shiryaev, The Theory of Martingales [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  2. S. Ya. Makhno, “Sufficient conditions for the convergence of solutions of stochastic equations,” Teor. Sluchain. Protessov, No. 16, 66–72 (1988).

    Google Scholar 

  3. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).

    Google Scholar 

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

    Google Scholar 

  5. D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin (1979).

    Google Scholar 

  6. A. Yu. Veretennikov, “Strong solutions of stochastic differential equations,” Teor. Veroyatn. i Primen.,24, No. 2, 348–360 (1979).

    Google Scholar 

  7. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  8. A. Yu. Veretennikov, “Strong and weak solutions of homogeneous stochastic equations with boundary conditions,” Teor. Veroyatn. i Primen.,26, No. 4, 685–701 (1981).

    Google Scholar 

  9. N. V. Krylov, Diffusion-Type Control Processes [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  10. Yu. A. Alkhutov and I. T. Mamedov, “The first boundary-value problem for nondivergence second-order parabolic equations with discontinuous coefficients,” Mat. Sb.,131, No. 4, 477–500 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukraine, Donetsk

    S. Ya. Makhno

Authors
  1. S. Ya. Makhno
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 284–289, February, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makhno, S.Y. Convergence of diffusion processes. Ukr Math J 44, 249–254 (1992). https://doi.org/10.1007/BF01061751

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01061751

Keywords

Search

Navigation