Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the mi...Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.展开更多
The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical di...The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).展开更多
This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm...This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.展开更多
In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
基金the National Natural Sciences Foundation of China the Foundation of Y.D. Fok.
文摘Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.
文摘The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).
基金Supported by NSFC(Grants Nos.11671115,11731012 and 11871425)NSF(Grant No.DMS-1855185)
文摘This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10131040)China Postdoctoral Science Foundation.
文摘In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
基金The work is supported by NSFC(No.11661025)Science Research Foundation of Guangxi Education department(No.YB2014117)+1 种基金Guangxi Programme for Promoting Young Teachers's Ability(No.2017KY0191)Innovative Programme for University(No.201510595198)
