| 随机Volterra-Levin方程解的存在唯一性与稳定性 |
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| 引用本文： | 郭利芳,朱全新. 随机Volterra-Levin方程解的存在唯一性与稳定性[J]. 宁波大学学报(理工版), 2011, 24(4): 56-59 |
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| 作者姓名： | 郭利芳 朱全新 |
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| 作者单位： | 宁波大学理学院,浙江宁波,315211 |
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| 基金项目： | 国家自然科学基金，宁波市自然科学基金 |
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| 摘 要： | 应用逐次逼近法研究了随机Volterra—Levin方程解的存在性，并结合H61der不等式证明了该方程解的唯一性与稳定性．最后用2个例子说明所获结果的有效性，同时表明条件“存在常数m〉0,使得∫-L^0p（s）ds=m”和“对所有的t≥0，∫0^1 e^4amsσ^2（t）ds/e^4amt都有界”是对Luo提出的条件进行了改进．
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| 关 键 词： | 逐次逼近法 随机Volterra-Levin方程 存在性 唯一性 稳定性 |
Existence, Uniqueness and Stability of Stochastic Volterra-Levin Equation |
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| GUO Li-fang,ZHU Quan-xin. Existence, Uniqueness and Stability of Stochastic Volterra-Levin Equation[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2011, 24(4): 56-59 |
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| Authors: | GUO Li-fang ZHU Quan-xin |
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| Affiliation: | GUO Li-fang,ZHU Quan-xin(Faculty of Science,Ningbo University,Ningbo 315211,China) |
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| Abstract: | Using the method of successive approximations, the existence of the solution for stochastic Volterra-Levin equations is obtained. Also, based on the H61der inequality, the solution is proven unique and stable. Finally, two examples show that the proposed conditions ＂there exists a constant m 〉 0, such that ∫-L^0p（s）ds=m＂ and ＂t≥0,∫0^1 e^4amsσ^2（t）ds/e^4amt is bounded for all t≥0＂generalize and improve those given in Luo＇s paper. |
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| Keywords: | successive approximations stochastic Volterra-Levin equations existence uniqueness stability |
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