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Backward Doubly Stochastic Integral Equations of the Volterra Type and Some Related Problems

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Abstract

Backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short) are observed in this paper. Existence of M-solution established under functional Lipschitz assumptions. Duality principle between linear BDSIEVs and (forward) stochastic Volterra integral equations is obtained. Using duality principle, the comparison theorem for the adapted solutions of BDSIEVs is proven.

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Correspondence to Jasmina Đorđević.

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Supported by Grant STORM-Stochastics for Time-Space Risk Models, granted by Research Council of Norway - Independent projects: ToppForsk. Project nr. 274410.

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Đorđević, J. Backward Doubly Stochastic Integral Equations of the Volterra Type and Some Related Problems. Commun. Math. Stat. (2023). https://doi.org/10.1007/s40304-023-00349-3

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  • DOI: https://doi.org/10.1007/s40304-023-00349-3

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