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Conditional central limit theorems for a sequence of conditional independent random variables
De-Mei Yuan,Li-Ran Wei,Lan Lei 대한수학회 2014 대한수학회지 Vol.51 No.1
A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.
De-Mei Yuan,Shun-Jing Li 대한수학회 2015 대한수학회지 Vol.52 No.2
Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in Lp for conditionally independent and conditionally identically distributed random variables are established, respectively.
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES
De-Mei Yuan,Xue-Mei Hu,Bao Tao 대한수학회 2014 대한수학회지 Vol.51 No.3
From the ordinary notion of uniformly strong mixing for a se- quence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mix- ing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by condi- tionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing ran- dom variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of condi- tional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.
De-Mei Yuan 대한수학회 2016 대한수학회지 Vol.53 No.6
The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.
CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES
Yuan, De-Mei,Wei, Li-Ran,Lei, Lan Korean Mathematical Society 2014 대한수학회지 Vol.51 No.1
A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.
Yuan, De-Mei,Li, Shun-Jing Korean Mathematical Society 2015 대한수학회지 Vol.52 No.2
Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.
Yuan, De-Mei Korean Mathematical Society 2016 대한수학회지 Vol.53 No.6
The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES
Yuan, De-Mei,Hu, Xue-Mei,Tao, Bao Korean Mathematical Society 2014 대한수학회지 Vol.51 No.3
From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.
Yin, Yong-Mei,Cui, Fu-De,Kim, Jung Sun,Choi, Min-Koo,Choi, Byung Chul,Chung, Suk-Jae,Shim, Chang-Koo,Kim, Dae-Duk Academic Press ; Taylor Francis 2009 DRUG DELIVERY Vol.16 No.1
<P>A redispersible dry emulsion (DE) formulation of atorvastatin calcium (AC) was developed to enhance the in vitro dissolution of AC, thereby increasing its gastrointestinal absorption. The spray-drying technology was used where Plurol Oleique CC 497 was chosen as the oil phase. Effects of carriers, surfactants, and homogenizers on the characteristics of DE containing AC were systematically investigated. The final formulation consisted of dextrin and Poloxamer 188 as carrier and surfactant, respectively, and was homogenized by a high pressure homogenizer before spray drying. The in vitro release of AC from the optimized DE was significantly higher than that of pure AC powder (76% vs. 30% at 24 hr). The in vitro intestinal absorption of AC from the DE formulation was 0.77 microg/cm(2) at 2 hr, which was a 2.33-fold increase compared to the pure unformulated AC powder. These results suggest that the oral dry emulsion formulation could improve the intestinal absorption of AC.</P>