In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square expo...In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square exponential stability of the analytic solutions for SVIDEs driven by L´evy noise are considered.The split-step theta method of SVIDEs driven by L´evy noise is proposed.The boundedness of the numerical solution and strong convergence are proved.Moreover,its mean square exponential stability is obtained.Some numerical examples are given to support the theoretical results.展开更多
基金supported by the Natural Science Foundation of Heilongjiang Province(Grant No.LH2022A020).
文摘In this paper,we investigate the theoretical and numerical analysis of the stochastic Volterra integro-differential equations(SVIDEs)driven by L´evy noise.The existence,uniqueness,boundedness and mean square exponential stability of the analytic solutions for SVIDEs driven by L´evy noise are considered.The split-step theta method of SVIDEs driven by L´evy noise is proposed.The boundedness of the numerical solution and strong convergence are proved.Moreover,its mean square exponential stability is obtained.Some numerical examples are given to support the theoretical results.
