Symmetrical martingale solutions of backward doubly stochastic Volterra integral equations. (English) Zbl 1460.60058
Summary: This paper aims to study a new class of integral equations called backward doubly stochastic Volterra integral equations (BDSVIEs, for short). The notion of symmetrical martingale solutions (SM-solutions, for short) is introduced for BDSVIEs. And the existence and uniqueness theorem for BDSVIEs in the sense of SM-solutions is established.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G44 | Martingales with continuous parameter |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Keywords:
backward doubly stochastic Volterra integral equation; backward stochastic integral; symmetrical martingale solutionReferences:
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