In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate devi...In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.展开更多
We consider harmonic moments of branching processes in general random environments. For a sequence of square integrable random variables, we give some conditions such that there is a positive constant c that every var...We consider harmonic moments of branching processes in general random environments. For a sequence of square integrable random variables, we give some conditions such that there is a positive constant c that every variable in this sequence belong to Ac or A1c uniformly.展开更多
Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing ...Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.展开更多
We consider non-extinct branching processes in general random environments. Under the condition of means and second moments of each generation being bounded, we give the upper bounds and lower bounds for some form dev...We consider non-extinct branching processes in general random environments. Under the condition of means and second moments of each generation being bounded, we give the upper bounds and lower bounds for some form deviations of the process.展开更多
We consider a discrete time random environment. We state that when the random walk on real number space in a environment is i.i.d., under the law, the law of large numbers, iterated law and CLT of the process are corr...We consider a discrete time random environment. We state that when the random walk on real number space in a environment is i.i.d., under the law, the law of large numbers, iterated law and CLT of the process are correct space-time random marginal annealed Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.展开更多
基金supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20231435)Fundamental Research Funds for the Central Universities(Grant No.NS2022069)supported by Natural Science Foundation of Zhejiang Province(Grant No.LY19A010004)。
文摘In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.
基金Supported by National Natural Science Foundtation of China (Grant No. 10771185)
文摘We consider harmonic moments of branching processes in general random environments. For a sequence of square integrable random variables, we give some conditions such that there is a positive constant c that every variable in this sequence belong to Ac or A1c uniformly.
基金Supported by the Humanities and Social Sciences Research Project of Ministry of Education(Grant No.18YJA910001)the National Natural Science Foundation of China(Grant No.11371321)the first author is also supported by the Education and Scientific Research Foundation for Young and Middle-aged teachers of Fujian Province(Grant No.B17154)
文摘Let X = {X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.
基金Supported by National Natural Science Foundation of China （Grant No. 11026088）, Zhejiang Provincial Natural Science Foundation of China （Grant No. Y6100663）, ZJPEDF （Grant No. Y200906909）
文摘We consider non-extinct branching processes in general random environments. Under the condition of means and second moments of each generation being bounded, we give the upper bounds and lower bounds for some form deviations of the process.
基金the National Natural Science Fundation of China (10371092)the Foundation of Wuhan University
文摘We consider a discrete time random environment. We state that when the random walk on real number space in a environment is i.i.d., under the law, the law of large numbers, iterated law and CLT of the process are correct space-time random marginal annealed Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.
