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- W3215606952 abstract "In this paper, we provide variation of constants formulae for linear (forward) stochastic Volterra integral equations (SVIEs, for short) and linear Type-II backward stochastic Volterra integral equations (BSVIEs, for short) in the usual Itô's framework. For these purposes, we define suitable classes of stochastic Volterra kernels and introduce new notions of the products of adapted L2-processes. Observing the algebraic properties of the products, we obtain the variation of constants formulae by means of the corresponding resolvent. Our framework includes SVIEs with singular kernels such as fractional stochastic differential equations. Also, our results can be applied to general classes of SVIEs and BSVIEs with infinitely many iterated stochastic integrals. The duality principle between generalized SVIEs and generalized BSVIEs is also proved." @default.
- W3215606952 created "2021-12-06" @default.
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- W3215606952 date "2023-01-01" @default.
- W3215606952 modified "2023-10-14" @default.
- W3215606952 title "Variation of constants formulae for forward and backward stochastic Volterra integral equations" @default.
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- W3215606952 doi "https://doi.org/10.1016/j.jde.2022.10.007" @default.
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