本文選題：隨機珊瑚礁模型　切入點：隨機過程　出處：《廣西師范學(xué)院》2017年碩士論文

【摘要】：在二十一世紀(jì),有關(guān)生物數(shù)學(xué)的研究越來越廣泛.然而,在現(xiàn)實生活中種群生態(tài)系統(tǒng)經(jīng)常會遇到各種環(huán)境白噪聲的干擾,因此,研究環(huán)境白噪聲是否對種群生態(tài)系統(tǒng)的動力學(xué)性質(zhì)產(chǎn)生一定的影響具有一定的理論和實際意義.因此,本文以隨機分析、隨機動力系統(tǒng)理論及統(tǒng)計學(xué)方法為工具來研究隨機珊瑚礁模型的漸近行為及參數(shù)估計問題具有一定的應(yīng)用價值和現(xiàn)實意義.主要研究內(nèi)容如下第一章詳細陳述了研究問題的背景及意義以及本文所要用到的一些預(yù)備知識,同時介紹了本學(xué)位論文研究的主要內(nèi)容及其框架結(jié)構(gòu).第二章主要研究隨機珊瑚礁模型的持久性與滅絕性.利用馬爾科夫理論、不變測度、遍歷性理論、大數(shù)定律及鞅不等式等相關(guān)理論,研究了隨機珊瑚礁模型解的尸階有界性、正解的存在性、解的正常返性及其平穩(wěn)分布,從而進一步研究了隨機珊瑚礁模型的持久性與滅絕性.第三章主要研究非線性噪聲驅(qū)動的隨機珊瑚礁模型的邊界漸近行為,利用隨機過程、邊界理論、概率測度、遍歷性理論及鞅理論等相關(guān)理論,首先研究隨機珊瑚礁模型相對應(yīng)的Fokker-Planck方程的解存在性,從而研究了隨機珊瑚礁模型的邊界漸近行為.其次,研究隨機珊瑚礁模型解的估計,進一步研究隨機珊瑚礁模型的共存問題.第四章主要研究隨機珊瑚礁模型的參數(shù)估計及其數(shù)值模擬.首先利用Euler離散化方法對模型進行離散化,然后再運用極大似然估計法的相關(guān)理論進行研究,得到了各個參數(shù)的估計結(jié)果,并且通過數(shù)值模擬驗證,這表明參數(shù)的極大似然估計的平方誤差依賴樣本的大小.然而,隨機變量在正態(tài)分布的假設(shè)下,各參數(shù)的極大似然估計值與真實值之間沒有明顯的差異,因此,各參數(shù)的極大似然估計值與真實值非常吻合.
[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.

【學(xué)位授予單位】：廣西師范學(xué)院
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

【參考文獻】

相關(guān)博士學(xué)位論文 前1條

1 蔣達清;隨機微分方程中的參數(shù)估計與假設(shè)檢驗問題[D];東北師范大學(xué);2006年

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本文編號：1705543