In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expec...In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.展开更多
Our aim in this note is to deal with boundary limits of monotone Sobolev functions with Δu∈Lp（·）logLq（·）（B）for the unit ball B Rn.Here p（·） and q（·） are variable exponents satisfying t...Our aim in this note is to deal with boundary limits of monotone Sobolev functions with Δu∈Lp（·）logLq（·）（B）for the unit ball B Rn.Here p（·） and q（·） are variable exponents satisfying the log-H61der and the log log-H61der conditions, respectively.展开更多
We prove the almost sure central limit theorems for the maxima of partial sums of r.v.＇s under a general condition of dependence due to Doukhan and Louhichi. We will separately consider the centered sequences and the...We prove the almost sure central limit theorems for the maxima of partial sums of r.v.＇s under a general condition of dependence due to Doukhan and Louhichi. We will separately consider the centered sequences and the sequences with positive expected values.展开更多
基金Supported by the National Natural Science Foundation of China(11771178)the Science and Technology Development Program of Jilin Province(20170101152JC)+1 种基金the Science and Technology Program of Jilin Edu-cational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)Fundamental Research Funds for the Central Universities。
文摘In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.
基金supported by Grant-in-Aid for Scientific Research (C) (Grant No. 21540183)Japan Society for the Promotion of Science
文摘Our aim in this note is to deal with boundary limits of monotone Sobolev functions with Δu∈Lp（·）logLq（·）（B）for the unit ball B Rn.Here p（·） and q（·） are variable exponents satisfying the log-H61der and the log log-H61der conditions, respectively.
文摘We prove the almost sure central limit theorems for the maxima of partial sums of r.v.＇s under a general condition of dependence due to Doukhan and Louhichi. We will separately consider the centered sequences and the sequences with positive expected values.
