| 一类随机泊松系统的解 |
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| 作者姓名： | 王余超 王丽瑾 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 100049 |
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| 基金项目： | National Natural Science Foundation of China (11971458, 11471310， and 11071251) |
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| 摘 要： | 考虑一类随机泊松系统，这类系统来自于对一类Lotka-Volterra系统进行Stratonovich型白噪声扰动。给出该系统的解几乎处处存在(全局不爆发)且唯一的充分条件，并进一步证明在这个条件下，解是几乎处处正的和有界的。数值实验对结论进行了验证。
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| 关 键 词： | 随机泊松系统 Lotka-Volterra系统 Stratonovich 型随机微分方程 不变量 不爆发 |
| 收稿时间： | 2020-07-16 |
| 修稿时间： | 2020-10-09 |
Solutions of a class of stochastic Poisson systems |
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| Authors: | WANG Yuchao WANG Lijin |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | In this paper, a class of stochastic Poisson systems, arising from randomly perturbing a type of Lotka-Volterra systems by certain Stratonovich white noise, are considered. We give the sufficient conditions for the almost sure existence (global non-explosion) and uniqueness of the solution of the system, and further prove that the solution is positive and bounded almost surely under the proposed conditions. Numeraical experiments are performed to verify the results. |
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| Keywords: | stochastic Poisson systems Lotka-Volterra systems Stratonovich SDEs invariants non-explosion |
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