Approximation of distributions of sums of weakly dependent random variables by the normal distribution
Copyright policy )Approximation of distributions of sums of weakly dependent random variables by the normal distribution
Let \(C^ 2\) be the collection of all real-valued functions defined on the real line R, which possess bounded continuous derivatives of the second order. For \(h\in C^ 2\), put \(\| h\|_ 2=\| h\| +\| h'\| +\| h''\|\), where \(\| h\| =\sup_{x\in R}| h(x)|.\) For an arbitrarily given natural integer n let \(X_ 1,...,X_ n\) be real-valued random variables with E \(X_ i=0\), E X\({}\) \(2_ i<\infty\), \(1\leq i\leq n\), and \(E(X_ 1+...+X_ n)\) \(2=1\). Put \[ S_ n=\sum^{n}_{i=1}X_ i,\quad F_ n(x)=P(S_ n
uniformly strong mixing, strong mixing, Central limit and other weak theorems, Convergence of probability measures, types of weak dependence
uniformly strong mixing, strong mixing, Central limit and other weak theorems, Convergence of probability measures, types of weak dependence
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