华东师范大学学报（自然科学版） >

2017 >Issue 4: 71 - 88

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.04.007

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随机吸烟模型的持久性与灭绝性

  • 张雪康 ,
  • 张振中
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  • 东华大学 数学系, 上海 201620
张雪康,男,硕士研究生,研究方向为随机分析及其应用.E-mail:xxkzhang@126.com.

收稿日期: 2016-05-18

  网络出版日期: 2017-07-20

基金资助

国家自然科学基金（11301068，11401093，11471071），东华大学非线性科学研究所基金

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Permanence and extinction of stochastic smoking model

  • ZHANG Xue-kang ,
  • ZHANG Zhen-zhong
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  • Department of Mathematics, Donghua University, Shanghai 201620, China

Received date: 2016-05-18

  Online published: 2017-07-20

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摘要

考虑随机因素的影响，提出了一个由布朗运动驱动的随机吸烟模型.首先，利用Lyapunov方法证明了随机吸烟模型具有全局正解性.其次，给出了该随机吸烟模型灭绝性和持久性的充分必要条件.最后运用伪极大似然方法估计出随机吸烟模型中的参数.

关键词： 布朗运动; 持久性; 灭绝性

本文引用格式

张雪康 , 张振中 . 随机吸烟模型的持久性与灭绝性[J]. 华东师范大学学报（自然科学版）, 2017 , (4) : 71 -88 . DOI: 10.3969/j.issn.1000-5641.2017.04.007

Abstract

To characterize the effects of stochastic noises on smokers, a stochastic smoking model driven by Brownian motion has been proposed. First, a unique global positive solution is proved according to Lyapunov function method. Then, some sufficient and necessary conditions for permanence and extinction are presented. Finally, the parameters of stochastic smoking model are estimated by the pseudo-maximum likelihood estimation.

Key words： Brownian motion; extinction; permanence

参考文献

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