Skip to main content
Log in

Proof of existence theorems for the two-parameter martingale problem

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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.

References

  1. V. M. Borodikhin, “An existence theorem for the two-parameter martingale problem,” in: Abstracts: The First World Congress of the Bernoulli Society for Mathematical Statistics and Probability Theory [in Russian], Nauka, Moscow, 1986,2, p. 652.

    Google Scholar 

  2. D. W. Stroock and S. R. S. Varadhan, “Diffusion processes with continuous coefficients,” Comm. Pure Appl. Math.,22, 345–400 (1969).

    Google Scholar 

  3. C. Tudor, “A theorem concerning the existence of the weak solution of the stochastic equation with continuous coefficients in the plane,” Rev. Roumaine Math. Pures Appl.,22, 1303–1308 (1977).

    Google Scholar 

  4. C. Tudor, “On the existence and the uniqueness of solutions to stochastic integral equations with two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,24, 817–827 (1979).

    Google Scholar 

  5. C. Tudor, “An invariance principle for Markov processes with two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,24, 1513–1523 (1979).

    Google Scholar 

  6. C. Tudor, “Remarks on the martingale problem in the two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,25, 1551–1556 (1980).

    Google Scholar 

  7. C. Tudor, “Stochastic integral equations in the plane,” Rev. Roumaine Math. Pures Appl.,26, 507–538 (1981).

    Google Scholar 

  8. V. M. Borodikhin, “On the martingale problem in the plane,” in: Limit Theorems of Probability Theory and Related Questions [in Russian], Nauka, Novosibirsk, 1982, pp. 146–156.

    Google Scholar 

  9. I. I. Gikhman and T. E. Pyasetskaya, “On a certain class of stochastic partial differential equations with two-parameter white noise,” in: Limit Theorems for Stochastic Processes [in Russian], Kiev, 1977, pp. 71–92.

  10. K. R. Parthasarathy, Probability Measures on Metric Spaces, Acad. Press, New York etc. (1967).

    Google Scholar 

  11. V. M. Borodikhin, “Density conditions for a family of measures in a certain space of two-parameter functions of Lipschitz type,” Sibirsk. Mat. Zh.,31, No. 4, 27–32 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Sibirskii Matemaiicheskii, Vol. 36, No. 2, pp. 248–265, March–April, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borodikhin, V.M. Proof of existence theorems for the two-parameter martingale problem. Sib Math J 36, 219–234 (1995). https://doi.org/10.1007/BF02110145

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02110145

Keywords

Navigation