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Some Properties of Solutions of Double Stochastic Differential Equations

Author

Listed:
  • C. Tudor

    (University of Bucharest and CIMAT)

  • M. Tudor

    (Academy of Economical Studies)

Abstract

The paper deals with double stochastic differential equations. Existence and uniqueness are obtained under a Hölder-type hypothesis. The convergence in probability of the successive approximations in the Hölder norm and the existence of a weak solution for continuous coefficients are also proved. Under an additional independence hypothesis, the mean square convergence of fractional step approximations is shown. This last result is used in order to deduce a comparison result and as a consequence the existence of a strong solution in the case when the ”double ”noise is additive.

Suggested Citation

  • C. Tudor & M. Tudor, 2002. "Some Properties of Solutions of Double Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 15(1), pages 129-151, January.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:1:d:10.1023_a:1013893301839
    DOI: 10.1023/A:1013893301839
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    References listed on IDEAS

    as
    1. Goncharuk, Nataliya Yu. & Kotelenez, Peter, 1998. "Fractional step method for stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 1-45, January.
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