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math.PR2019
Extension of Donsker's Invariance Principle with Incomplete Partial-Sum Process
Jingwei Liu
Based on deleting-item central limit theory, the classical Donsker's theorem of partial-sum process of independent and identically distributed (i.i.d.) random variables is extended…
math.PR2019★ 1 cited
Extension of Limit Theory with Deleting Items Partial Sum of Random Variable Sequence
Jingwei Liu
The deleting items theorems of weak law of large numbers (WLLN),strong law of large numbers (SLLN) and central limit theorem (CLT) are derived by substituting partial sum of random…
math.PR2012
Inequality for Variance of Weighted Sum of Correlated Random Variables and WLLN
Jingwei Liu
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with…