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This paper aims to study a new class of integral equations called backwarddoubly stochastic Volterra integral equations (BDSVIEs, for short). The notionof symmetrical martingale solutions (SM-solutions, for short) is introduced forBDSVIEs. And the existence and uniqueness theorem for BDSVIEs in the sense ofSM-solutions is established.

Symmetrical martingale solutions of backward doubly stochastic Volterra integral equations