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On Solutions of Backward Stochastic Volterra Integral Equations with Jumps in Hilbert Spaces

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Abstract

This paper studies the existence, uniqueness and stability of the adapted solutions to backward stochastic Volterra integral equations (BSVIEs) driven by a cylindrical Brownian motion on a separable Hilbert space and a Poisson random measure with non-Lipschitz coefficient. Moreover, a duality principle between the linear forward stochastic Volterra integral equations (FSVIEs) with jumps and the linear BSVIEs with jumps is established.

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Authors and Affiliations

  1. School of Mathematics, University of Tasmania, GPO Box 252C-37, Hobart, Tasmania, 7001, Australia

    Y. Ren

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  1. Y. Ren
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Correspondence to Y. Ren.

Additional information

Communicated by F. Zirilli.

This work was supported by the Discovery Project DP0770388 from the Australian Research Council. Also, the work was partially supported by National Natural Science Foundation of China and NSF of Anhui Educational Bureau (Project KJ2009A128).

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Ren, Y. On Solutions of Backward Stochastic Volterra Integral Equations with Jumps in Hilbert Spaces. J Optim Theory Appl 144, 319–333 (2010). https://doi.org/10.1007/s10957-009-9596-2

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  • DOI: https://doi.org/10.1007/s10957-009-9596-2

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