Advertisement

Siberian Mathematical Journal

, Volume 36, Issue 2, pp 219–234 | Cite as

Proof of existence theorems for the two-parameter martingale problem

  • V. M. Borodikhin
Article
  • 25 Downloads

Keywords

Existence Theorem Martingale Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 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. 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. 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. 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. 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. 7.
    C. Tudor, “Stochastic integral equations in the plane,” Rev. Roumaine Math. Pures Appl.,26, 507–538 (1981).Google Scholar
  8. 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. 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.Google Scholar
  10. 10.
    K. R. Parthasarathy, Probability Measures on Metric Spaces, Acad. Press, New York etc. (1967).Google Scholar
  11. 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

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. M. Borodikhin
    • 1
  1. 1.Novosibirsk

Personalised recommendations