随机珊瑚礁模型的渐近行为研究

发布时间：2018-04-03 14:13

本文选题：随机珊瑚礁模型　切入点：随机过程　出处：《广西师范学院》2017年硕士论文

【摘要】：在二十一世纪,有关生物数学的研究越来越广泛.然而,在现实生活中种群生态系统经常会遇到各种环境白噪声的干扰,因此,研究环境白噪声是否对种群生态系统的动力学性质产生一定的影响具有一定的理论和实际意义.因此,本文以随机分析、随机动力系统理论及统计学方法为工具来研究随机珊瑚礁模型的渐近行为及参数估计问题具有一定的应用价值和现实意义.主要研究内容如下第一章详细陈述了研究问题的背景及意义以及本文所要用到的一些预备知识,同时介绍了本学位论文研究的主要内容及其框架结构.第二章主要研究随机珊瑚礁模型的持久性与灭绝性.利用马尔科夫理论、不变测度、遍历性理论、大数定律及鞅不等式等相关理论,研究了随机珊瑚礁模型解的尸阶有界性、正解的存在性、解的正常返性及其平稳分布,从而进一步研究了随机珊瑚礁模型的持久性与灭绝性.第三章主要研究非线性噪声驱动的随机珊瑚礁模型的边界渐近行为,利用随机过程、边界理论、概率测度、遍历性理论及鞅理论等相关理论,首先研究随机珊瑚礁模型相对应的Fokker-Planck方程的解存在性,从而研究了随机珊瑚礁模型的边界渐近行为.其次,研究随机珊瑚礁模型解的估计,进一步研究随机珊瑚礁模型的共存问题.第四章主要研究随机珊瑚礁模型的参数估计及其数值模拟.首先利用Euler离散化方法对模型进行离散化,然后再运用极大似然估计法的相关理论进行研究,得到了各个参数的估计结果,并且通过数值模拟验证,这表明参数的极大似然估计的平方误差依赖样本的大小.然而,随机变量在正态分布的假设下,各参数的极大似然估计值与真实值之间没有明显的差异,因此,各参数的极大似然估计值与真实值非常吻合.
[Abstract]:In twenty-first Century, the study about mathematical biology more and more widely. However, interference in the real life of populations and ecosystems often encounter a variety of environmental noise and white noise is research on environmental dynamics of population ecology influence has certain theoretical and practical significance. Therefore, based on the stochastic analysis asymptotic behavior and parameters of random dynamical system theory and statistical methods as a tool to study the random reef estimation model has certain application value and practical significance. The main contents are as follows some preliminaries first chapter introduced the research background and significance of this paper and will be used at the same time, introduced the main contents of this thesis the research and the frame structure. The second chapter mainly studies the persistence and extinction of random coral reef model. By Marco Fu theory, invariant measure, ergodic theory, the law of large numbers and martingale inequalities and other related theories, research on the dead order solutions of stochastic coral reef model boundedness, the existence of positive solutions, recurrent and stationary distribution solutions, in order to further study the stochastic model of coral reef persistence and extinction asymptotic behavior of random boundary. Coral reef model driven the third chapter mainly studies the nonlinear noise, using stochastic process, boundary theory, probability measure, ergodic theory and the martingale theory, the existence of solutions of the Fokker-Planck equation first random model corresponding to the coral reefs, so as to study the asymptotic behavior of stochastic boundary reef model. Secondly, study on estimation of random reef model solution, the coexistence of the further research of coral reef stochastic model. The parameter estimation and numerical simulation the fourth chapter mainly studies the stochastic model of coral reefs. We use Euler discretization method is used to discretize the model, and then use the theory of maximum likelihood estimation method of parameters estimation results obtained, and verified by numerical simulation, which indicates that the square error of maximum likelihood estimation of the parameters depend on the sample size. However, the random variables in the hypothesis of normal distribution next, the maximum likelihood estimates of the parameters had no obvious difference between the true value and, therefore, the maximum likelihood estimates of the parameters are in good agreement with the true value.

【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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