一类随机泊松系统的解  

Solutions of a class of stochastic Poisson systems

作　　者：王余超 王丽瑾 WANG Yuchao;WANG Lijin(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2022年第6期721-726,共6页Journal of University of Chinese Academy of Sciences

基　　金：Supported by National Natural Science Foundation of China(11971458,11471310,and 11071251)。

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。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.

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 

分 类 号：O241.8[理学—计算数学]