MEAN-FIELD BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

    Authors

    Y. F. Shi; T. X. Wang;J. M. Yong

    Comments

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    Abbreviated Journal Title

    Discrete Contin. Dyn. Syst.-Ser. B

    Keywords

    Mean-field stochastic Volterra integral equation; mean-field backward; stochastic Volterra integral equation; duality principle; maximum; principle; MCKEAN-VLASOV EQUATION; HILBERT-SPACE; DIFFERENTIAL-EQUATION; EVOLUTION; EQUATION; ADAPTED SOLUTION; LIMIT; DIFFUSIONS; REGULARITY; DYNAMICS; Mathematics, Applied

    Abstract

    Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted M-solutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. A Pontryagin's type maximum principle is established for an optimal control of MF-FSVIEs.

    Journal Title

    Discrete and Continuous Dynamical Systems-Series B

    Volume

    18

    Issue/Number

    7

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    1929

    Last Page

    1967

    WOS Identifier

    WOS:000319859800011

    ISSN

    1531-3492

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