We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its...We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its position in Zd,denoted by Xt. Note that the whole space is not homogeneous. We define the environment process viewed from the tagged particle, of which Xt can be expressed as a functional. It is called the tagged particle process. We show the ergodicity of the tagged particle process, then prove the strong law of large numbers. Furthermore, we show the central limit theorem of Xt provided the zero-mean condition.展开更多
In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the...In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11371040)
文摘We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its position in Zd,denoted by Xt. Note that the whole space is not homogeneous. We define the environment process viewed from the tagged particle, of which Xt can be expressed as a functional. It is called the tagged particle process. We show the ergodicity of the tagged particle process, then prove the strong law of large numbers. Furthermore, we show the central limit theorem of Xt provided the zero-mean condition.
基金Project supported by the Yunnan Provincial Natural Science Foundation of China(No.00A0006R).
文摘In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.
