Comparison between criteria leading to the weak invariance principle
نویسندگان
چکیده
Abstract. The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR 188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields 110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist. 36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab. 28 (2000) later improved upon by Peligrad and Utev in Ann. Probab. 33 (2005). We prove that in every ergodic dynamical system with positive entropy, if we consider two of these criteria, we can find a function in L satisfying the first but not the second.
منابع مشابه
Independence of Four Projective Criteria for the Weak Invariance Principle
Let (Xi)i∈Z be a regular stationary process for a given filtration. The weak invariance principle holds under the condition ∑ i∈Z ‖P0(Xi)‖2 < ∞ (see [11], [2], [3]). In this paper, we show that this criterion is independent of other known criteria: the martingalecoboundary decomposition of Gordin (see [7], [8]), the criterion of Dedecker and Rio (see [4]) and the condition of Maxwell and Woodro...
متن کاملComparison of Quenched and Annealed Invariance Principles for Random Conductance Model: Part Ii
We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold. In the present paper we give a proof of the full scaling limit for the weak invariance principle, improving the result in an earlier paper where we obtained a subsequential limit.
متن کاملComparison of Quenched and Annealed Invariance Principles for Random Conductance Model
We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold.
متن کاملEvaluation and Comparison of LEED, BREEAM, and the 19th issue of National Building Regulations of Iran (NBRI) in Perspective of Sustainability by (MCDM) TOPSIS Method
In this research, the features of LEED, BREEAM, and NBRI also, their principles, are reviewed, evaluated, and compared from the aspects of the sustainability. The compliance items of standards with the principles of sustainability determine that their goals are well matched. By comparing the different and shared principles, it discovered how each standard has succeeded from the aspect of the su...
متن کاملInvariance principle for stochastic processes with short memory
Abstract: In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the weak invariance principle for partial sums of linear processes with short memory. We prove that whenever the partial sums of innovations satisfy th...
متن کامل