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SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS
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 Title & Authors
SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS
Shi, Yufeng; Wang, Tianxiao;
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 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;
 Language
English
 Cited by
1.
Mean-field backward stochastic Volterra integral equations, Discrete and Continuous Dynamical Systems - Series B, 2013, 18, 7, 1929  crossref(new windwow)
2.
Optimal control problems of forward-backward stochastic Volterra integral equations, Mathematical Control and Related Fields, 2015, 5, 3, 613  crossref(new windwow)
3.
An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
4.
Backward stochastic Volterra integral equations — a brief survey, Applied Mathematics-A Journal of Chinese Universities, 2013, 28, 4, 383  crossref(new windwow)
5.
Backward stochastic Volterra integral equations with additive perturbations, Applied Mathematics and Computation, 2015, 265, 903  crossref(new windwow)
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