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Some Properties of Solutions of Double Stochastic Differential Equations

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest and CIMAT, Str. Academiei 14, 70109, Bucharest, Romania

    C. Tudor

  2. Department of Mathematics, Academy of Economical Studies, 70167, Bucharest, Romania

    M. Tudor

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  1. C. Tudor
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  2. M. Tudor
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Correspondence to C. Tudor.

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Tudor, C., Tudor, M. Some Properties of Solutions of Double Stochastic Differential Equations. Journal of Theoretical Probability 15, 129–151 (2002). https://doi.org/10.1023/A:1013893301839

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