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http://dx.doi.org/10.4134/JKMS.2012.49.6.1301

SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS  

Shi, Yufeng (School of Mathematics Shandong University)
Wang, Tianxiao (School of Mathematics Shandong University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.6, 2012 , pp. 1301-1321 More about this Journal
Abstract
In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14] and [15].
Keywords
backward stochastic Volterra integral equations; adapted solutions; adapted M-solutions; non-Lipschitz conditions; stochastic Lipschitz coefficients;
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