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Quasi-stationary Distributions And Rates Of Convergence For One-dimensional Diffusions

Posted on:2017-06-24Degree:MasterType:Thesis
Country:ChinaCandidate:Y J ZhangFull Text:PDF
GTID:2347330485965081Subject:Statistics
Abstract/Summary:PDF Full Text Request
The quasi-stationary distributions of Markov processes have been becoming an active research area. The quasi-stationary distributions of one dimentional diffusions and related issues has not been researched consummate. In this paper, we mainly study quasi-stationary distributions for one-dimensional diffusions.In the first chapter, we will introduce the research background and the re-search status of quasi-stationary distributions. we will give the main results of this paper.In the second chapter, the basic theory of the one dimensional diffusions and QSDs will be introduced.In the third chapter, we study QSDs for one-dimensional diffusions under the condition that 0 is a exit boundary and oo is a natural boundary. When 0 is a exit boundary and oo is a natural boundary,we give a necessary condition for the existence of a QSD.In the fourth chapter, we will work out the speed of convergence to the quasi-stationary distribution for Ornstein-Uhlenbeck process.
Keywords/Search Tags:One-dimensional diffusions, quasi-stationary distribution, domain of attraction, natural boundary, exit boundary, speed of convergence
PDF Full Text Request
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